Interactivity API: Use Script Module filter to pass data to the client

[jonsurrell]

​Proposal: Server to client data sharing for Script Modules describes an API for passing data to Script Modules.

This API was introduced in [58579].

Interactivity API currently uses its own mechanism to do the same thing. Instead of its own implementation, it should use the new Core API.

## ⚠️ This is follow-up work to PR #6682.

Use the work in #6682 for Interactivity API script module data (passing store and config data to the client).

Depends on (includes) #6682.

Todo:

• [ ] All of the print/encode tests can be removed (that testing is now part of #6682).
• [ ] Add tests on the filter being used correctly.

This will not work until client scripts are updated. The @wordpress/interactivity Script Module was updated in ​https://github.com/WordPress/gutenberg/pull/61658 to try to get client data from an updated element ID. This requires @wordpress/interactivity@>5.7.0.

Trac ticket: https://core.trac.wordpress.org/ticket/61512

@luisherranz @cbravobernal @darerodz I'd love to get an Interactivity API review of this 🙏

Suggested commit message:

Interactivity API: Use Script Modules filter for store and config data

A dedicated API exists for passing data to Script Modules implemented in
changeset [58579]. Use this Core API instead of a custom implementation
for Interactivity API to pass data to the client.

Props jonsurrell, gziolo, luisherranz, cbravobernal.
Fixes #61512.

[Bernhard Reiter]

In 58729:

Interactivity API: Use Script Modules filter for store & config data.

A dedicated API exists for passing data to Script Modules implemented in changeset [58579].
Use this Core API instead of a custom implementation for Interactivity API to pass data to the client.

Developed in ​https://github.com/WordPress/wordpress-develop/pull/6683.

Props jonsurrell, gziolo, luisherranz, cbravobernal.
Fixes #61512.

Committed to Core in https://core.trac.wordpress.org/changeset/58729.