You can actually use user:[user]/Module:foo to test Modules while developing them using the https://en.m.wikipedia.org/wiki/Special:TemplateSandbox

Amm, actually, the PR mentioned above has been merged. So declined status isn't appropriate:)
I'm sorry I forgot to notify here.

I sent a patch ( https://gerrit.wikimedia.org/r/#/c/mediawiki/extensions/Scribunto/+/501940/ )
using Gerrit Patch Uploader (wikitech account creating is currently disabled).

Thank you!
It seems to solve my problem. There is a question however wheter or not it should be Parser function.

I have submited a pull request https://github.com/wikimedia/apps-android-wikipedia/pull/123.

Acctually I have already implemented that solution and it works great! I'll be happy to contribute it to the github repo, but as I read I should wait until it will get out of open tasks/needs triage category, am I right?

Well, I posted a possible solution.

Well, I checked it a bit and discovered that the decision whether a page is lua is in the scribunto extension in /includes/common/Hooks.php
in the function: contentHandlerDefaultModelFor

public static function contentHandlerDefaultModelFor( Title $title, &$model ) {
	if ( $model === 'sanitized-css' ) {
		// Let TemplateStyles override Scribunto
		return true;
	}
	if ( $title->getNamespace() == NS_MODULE && !Scribunto::isDocPage( $title ) ) {
		$model = CONTENT_MODEL_SCRIBUNTO;
		return true;
	}
	return true;
}

actually in my version of mediawiki(1.32.0) is

public static function contentHandlerDefaultModelFor( Title $title, &$model ) {
	if ( $title->getNamespace() == NS_MODULE && !Scribunto::isDocPage( $title ) ) {
		$model = CONTENT_MODEL_SCRIBUNTO;
		return false;
	}
	return true;
}

maybe scribunto is related too.

I'm sorry, I'm new here, but how things are usually going here?
I mean, how the decisions are made and who does the work of writing/fixing the code of mediawiki extensions?

Isn't it possible to get the wikicode of specific section and render just it?
like when you edit a specific section.