Update code and tests for theme json class after the back port in core

[tellthemachines]

What?

Applies the improvements from the style variations backport PR back into Gutenberg.

Why?

It make things better.

How?

Testing Instructions

Make sure the changes from #47134 still work;
Run PHP unit tests and make sure they pass.

Testing Instructions for Keyboard

Screenshots or screencast

[github-actions]

Flaky tests detected in e39e451.
Some tests passed with failed attempts. The failures may not be related to this commit but are still reported for visibility. See the documentation for more information.

🔍 Workflow run URL: https://github.com/WordPress/gutenberg/actions/runs/4071174543
📝 Reported issues:

• [Flaky Test] List #47632 in specs/editor/blocks/query.test.js
• [Flaky Test] should display (capture the) text from the currently active link even if there is a rich text selection #36495 in specs/editor/various/links.test.js
• [Flaky Test] should write over selection #39938 in specs/editor/various/multi-block-selection.test.js

[ntsekouras]

Thank you!