This PR contributes to https://github.com/flutter/flutter/issues/130459
### Description
- Updates `examples/api/lib/material/tab_controller/tab_controller.1.dart` to properly remove the listener from the `TabController`
- Adds tests for `examples/api/lib/material/tab_controller/tab_controller.1.dart`
This does a cleanup of the examples, removing all of the "section" markers and extra comments that we don't need anymore now that the samples are no longer in the source code. It also removes the --template arguments from the {@tool dartpad} and {@tool sample} directives, since those are no longer used. It converts two examples that I discovered were still embedded into linked examples in the examples folder.
I didn't delete the templates from the snippets config folder yet, because there are still embedded samples in the dart:ui package from the engine that use them. Once dart:ui no longer uses the templates, they can be removed.
I bumped the version of the snippets package to pick up a change that allows removal of the --template argument.
This extracts the sample code out from the API doc comments, and places them in separate files on disk, allowing running of the examples locally, testing them, and building of slightly larger examples.
