With this logback.xml:

<?xml version="1.0" encoding="UTF-8"?>
<configuration debug="true">
    <include resource="org/springframework/boot/logging/logback/base.xml" />
    <springProperty scope="context" name="appName" source="spring.application.name"/>

    <appender name="LOKI" class="com.github.loki4j.logback.Loki4jAppender">
        <verbose>true</verbose>
        <http>
            <url>http://localhost:3100/loki/api/v1/push</url>
        </http>
        <format>
            <label>
                <pattern>app=${appName},host=${HOSTNAME},traceID=%X{traceId:-NONE},level=%level</pattern>
            </label>
            <message>
                <pattern>${FILE_LOG_PATTERN}</pattern>
            </message>
            <sortByTime>true</sortByTime>
        </format>
    </appender>

    <root level="INFO">
        <appender-ref ref="LOKI"/>
    </root>
</configuration>

You get these errors on startup:

12:13:01,634 |-ERROR in ch.qos.logback.core.model.processor.ImplicitModelHandler - Could not create component [http] of type [null] java.lang.NoSuchMethodException: com.github.loki4j.logback.JavaHttpSender.<init>()
    at java.lang.NoSuchMethodException: com.github.loki4j.logback.JavaHttpSender.<init>()
    at  at java.base@17.0.5/java.lang.Class.getConstructor0(DynamicHub.java:3585)
    at  at java.base@17.0.5/java.lang.Class.getConstructor(DynamicHub.java:2271)
    at  at ch.qos.logback.core.model.processor.ImplicitModelHandler.doComplex(ImplicitModelHandler.java:154)
    at  at ch.qos.logback.core.model.processor.ImplicitModelHandler.handle(ImplicitModelHandler.java:94)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:241)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:253)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:253)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.traversalLoop(DefaultProcessor.java:90)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.process(DefaultProcessor.java:106)
    at  at ch.qos.logback.core.joran.GenericXMLConfigurator.processModel(GenericXMLConfigurator.java:200)
    at  at org.springframework.boot.logging.logback.SpringBootJoranConfigurator.processModel(SpringBootJoranConfigurator.java:112)
    at  at org.springframework.boot.logging.logback.SpringBootJoranConfigurator.configureUsingAotGeneratedArtifacts(SpringBootJoranConfigurator.java:105)
    at  at org.springframework.boot.logging.logback.LogbackLoggingSystem.initializeFromAotGeneratedArtifactsIfPossible(LogbackLoggingSystem.java:208)
    at  at org.springframework.boot.logging.logback.LogbackLoggingSystem.initialize(LogbackLoggingSystem.java:185)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.initializeSystem(LoggingApplicationListener.java:332)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.initialize(LoggingApplicationListener.java:298)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.onApplicationEnvironmentPreparedEvent(LoggingApplicationListener.java:246)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.onApplicationEvent(LoggingApplicationListener.java:223)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.doInvokeListener(SimpleApplicationEventMulticaster.java:176)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.invokeListener(SimpleApplicationEventMulticaster.java:169)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.multicastEvent(SimpleApplicationEventMulticaster.java:143)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.multicastEvent(SimpleApplicationEventMulticaster.java:131)
    at  at org.springframework.boot.context.event.EventPublishingRunListener.multicastInitialEvent(EventPublishingRunListener.java:136)
    at  at org.springframework.boot.context.event.EventPublishingRunListener.environmentPrepared(EventPublishingRunListener.java:82)
    at  at org.springframework.boot.SpringApplicationRunListeners.lambda$environmentPrepared$2(SpringApplicationRunListeners.java:64)
    at  at java.base@17.0.5/java.lang.Iterable.forEach(Iterable.java:75)
    at  at org.springframework.boot.SpringApplicationRunListeners.doWithListeners(SpringApplicationRunListeners.java:118)
    at  at org.springframework.boot.SpringApplicationRunListeners.doWithListeners(SpringApplicationRunListeners.java:112)
    at  at org.springframework.boot.SpringApplicationRunListeners.environmentPrepared(SpringApplicationRunListeners.java:63)
    at  at org.springframework.boot.SpringApplication.prepareEnvironment(SpringApplication.java:355)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:306)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:1304)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:1293)
    at  at com.example.demo.DemoAotNativeApplication.main(DemoAotNativeApplication.java:10)
12:13:01,635 |-ERROR in ch.qos.logback.core.model.processor.ImplicitModelHandler - Could not create component [format] of type [null] java.lang.NoSuchMethodException: com.github.loki4j.logback.JsonEncoder.<init>()
    at java.lang.NoSuchMethodException: com.github.loki4j.logback.JsonEncoder.<init>()
    at  at java.base@17.0.5/java.lang.Class.getConstructor0(DynamicHub.java:3585)
    at  at java.base@17.0.5/java.lang.Class.getConstructor(DynamicHub.java:2271)
    at  at ch.qos.logback.core.model.processor.ImplicitModelHandler.doComplex(ImplicitModelHandler.java:154)
    at  at ch.qos.logback.core.model.processor.ImplicitModelHandler.handle(ImplicitModelHandler.java:94)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:241)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:253)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.secondPhaseTraverse(DefaultProcessor.java:253)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.traversalLoop(DefaultProcessor.java:90)
    at  at ch.qos.logback.core.model.processor.DefaultProcessor.process(DefaultProcessor.java:106)
    at  at ch.qos.logback.core.joran.GenericXMLConfigurator.processModel(GenericXMLConfigurator.java:200)
    at  at org.springframework.boot.logging.logback.SpringBootJoranConfigurator.processModel(SpringBootJoranConfigurator.java:112)
    at  at org.springframework.boot.logging.logback.SpringBootJoranConfigurator.configureUsingAotGeneratedArtifacts(SpringBootJoranConfigurator.java:105)
    at  at org.springframework.boot.logging.logback.LogbackLoggingSystem.initializeFromAotGeneratedArtifactsIfPossible(LogbackLoggingSystem.java:208)
    at  at org.springframework.boot.logging.logback.LogbackLoggingSystem.initialize(LogbackLoggingSystem.java:185)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.initializeSystem(LoggingApplicationListener.java:332)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.initialize(LoggingApplicationListener.java:298)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.onApplicationEnvironmentPreparedEvent(LoggingApplicationListener.java:246)
    at  at org.springframework.boot.context.logging.LoggingApplicationListener.onApplicationEvent(LoggingApplicationListener.java:223)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.doInvokeListener(SimpleApplicationEventMulticaster.java:176)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.invokeListener(SimpleApplicationEventMulticaster.java:169)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.multicastEvent(SimpleApplicationEventMulticaster.java:143)
    at  at org.springframework.context.event.SimpleApplicationEventMulticaster.multicastEvent(SimpleApplicationEventMulticaster.java:131)
    at  at org.springframework.boot.context.event.EventPublishingRunListener.multicastInitialEvent(EventPublishingRunListener.java:136)
    at  at org.springframework.boot.context.event.EventPublishingRunListener.environmentPrepared(EventPublishingRunListener.java:82)
    at  at org.springframework.boot.SpringApplicationRunListeners.lambda$environmentPrepared$2(SpringApplicationRunListeners.java:64)
    at  at java.base@17.0.5/java.lang.Iterable.forEach(Iterable.java:75)
    at  at org.springframework.boot.SpringApplicationRunListeners.doWithListeners(SpringApplicationRunListeners.java:118)
    at  at org.springframework.boot.SpringApplicationRunListeners.doWithListeners(SpringApplicationRunListeners.java:112)
    at  at org.springframework.boot.SpringApplicationRunListeners.environmentPrepared(SpringApplicationRunListeners.java:63)
    at  at org.springframework.boot.SpringApplication.prepareEnvironment(SpringApplication.java:355)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:306)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:1304)
    at  at org.springframework.boot.SpringApplication.run(SpringApplication.java:1293)
    at  at com.example.demo.DemoAotNativeApplication.main(DemoAotNativeApplication.java:10)

It looks like some reflection hints that should have been derived from Logback's configuration model at build time are missing.