There has been a lot of changes recently with the release of the stable version. As stated in the release notes:

Json constructor is replaced with Json {} builder function, JsonConfiguration is deprecated in favor of Json {} builder

Your tutorial is outdated. I suggest you read the official docs instead.

As for dependencies, runtime was renamed to json in 1.0.0. You should have all of these:

// build.gradle
buildscript {
    repositories { 
        jcenter()
    }

    dependencies {
        classpath "org.jetbrains.kotlin:kotlin-serialization:$kotlinVersion"
    }
}

// app/build.gradle
plugins {
    id "org.jetbrains.kotlin.plugin.serialization"
}

dependencies {
    implementation "org.jetbrains.kotlinx:kotlinx-serialization-json:$serializationVersion"
}

The plugin is not sufficient to use Kotlinx Serialization, you also need the runtime library to use classes from the kotlinx.serialization.* packages. This is covered in the docs: https://github.com/Kotlin/kotlinx.serialization#dependency-on-the-json-library

In Gradle, this means you need to add Kotlinx serialization as a dependency in the dependencies block:

repositories {
    mavenCentral()
}

dependencies {
    implementation "org.jetbrains.kotlinx:kotlinx-serialization-json:1.2.1"
}

If you need other formats than JSON, you'll need to add the corresponding artifact instead.

I was able to resolve the warning "kotlinx.serialization compiler plugin is not applied to the module, so this annotation would not be processed. Make sure that you've setup your buildscript correctly and re-import project." by adding the serialization plugin in the project-level build.gradle.kts, and then applying it in the module-level build.gradle.kts.

Project build.gradle.kts:

plugins {
    ...    
    kotlin("plugin.serialization") version "1.9.0" apply false
}

Module build.gradle.kts:

plugins {
    ...
    kotlin("plugin.serialization")
}
...
dependencies {
    ...
    implementation("org.jetbrains.kotlinx:kotlinx-serialization-json:1.6.0")
}