In Gradle 8 (build tool) kts DSL, how to split sections that depends on KotlinBuildScript and plugins in a `build.gradle.kts` file into another file?

Question

Assuming that several Gradle projects are sharing the same plugin & buildScript settings:

buildscript {
    repositories {
        // Add here whatever repositories you're already using
        mavenCentral()
    }

    dependencies {
        classpath("ch.epfl.scala:gradle-bloop_2.12:1.4.13") // suffix is always 2.12, weird
    }
}

plugins {
//    base
    java
    `java-test-fixtures`

    scala
    kotlin("jvm") version "1.6.10" // TODO: remove?

    idea

    `maven-publish`
}

Both sections are declared under KotlinBuildScript:

@Deprecated("Will be removed in Gradle 9.0")
abstract class KotlinBuildScript(
    private val host: KotlinScriptHost<Project>
) : @Suppress("DEPRECATION") org.gradle.kotlin.dsl.support.delegates.ProjectDelegate() {
...

I would like to move them into a shared git submodule, a few online articles suggested that I should exploit the KotlinScript class extension feature and aggregate them into an extension like this, either under buildSrc directory (automatically included in KotlinScript interpretation classpath) or under the same build.gradle.kts script. All these articles use Project class as an example:

fun Project.xxx(): Versions {
}

But when I try to apply this solution to KotlinBuildScript, I got the following error:

// under build.gradle.kts
fun KotlinBuildScript.dummy(): Unit {}

dummy()

error:

build.gradle.kts:6:1: Unresolved reference. None of the following candidates is applicable because of receiver type mismatch: 
public final fun KotlinBuildScript.dummy(): Unit defined in Build_gradle

What's the cause of this error? If KotlinBuildScript is not the receiver (which still doesn't explain why buildscript & plugins are in script root scope), what should be used instead?

UPDATE 1: It appears that extensions to Project class only works under 1 condition: they have to be defined under build.gradle.kts, once moved into buildSrc, any invocation of Gradle plugin will cause a compilation error:

//under `buildSrc/.../init.kt`

fun Project.dummy2(): Unit {

    idea {
    }
}

this will cause the error:

e: file:///home/peng/git-proto/scaffold-gradle-kts/buildSrc/src/main/kotlin/init.kt:17:5 Expression 'idea' cannot be invoked as a function. The function 'invoke()' is not found
e: file:///home/peng/git-proto/scaffold-gradle-kts/buildSrc/src/main/kotlin/init.kt:17:5 Unresolved reference. None of the following candidates is applicable because of receiver type mismatch: 
public val PluginDependenciesSpec.idea: PluginDependencySpec defined in org.gradle.kotlin.dsl

FAILURE: Build failed with an exception.

So both extension fail, what should be done in these cases?

The described experiment and errors can be observed in the following project:

https://github.com/tribbloid/scaffold-gradle-kts/blob/cdb18cd40fa862aaf4cfea1af2f75165a186bd89/buildSrc/src/main/kotlin/init.kt