Post Settings: Support custom taxonomies

[crazytonyli]

Description

This PR allows updating the terms of custom taxonomies in posts. The feature requires application passwords and works on all sites where custom taxonomies are available.

Testing instructions

Verify all terms (including tags and categories) can be updated.

[dangermattic]

	2 Warnings
⚠️	View files have been modified, but no screenshot or video is included in the pull request. Consider adding some for clarity.
⚠️	This PR is larger than 500 lines of changes. Please consider splitting it into smaller PRs for easier and faster reviews.

Generated by 🚫 Danger

[sonarqubecloud]

Quality Gate passed

Issues
3 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[crazytonyli]

@kean I need to add similar code, like updating the new otherTerms variable, assigning its value to another instance, etc. I don't think I missed any places. But can you pay extra attention to reviewing this part? Thanks!

[wpmobilebot]

📲 You can test the changes from this Pull Request in WordPress by scanning the QR code below to install the corresponding build.

	App Name	WordPress
	Configuration	Release-Alpha
	Build Number	29620
	Version	PR #24964
	Bundle ID	org.wordpress.alpha
	Commit	f7098f8
	Installation URL	6k7p0dekkv9mg

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[wpmobilebot]

📲 You can test the changes from this Pull Request in Jetpack by scanning the QR code below to install the corresponding build.

	App Name	Jetpack
	Configuration	Release-Alpha
	Build Number	29620
	Version	PR #24964
	Bundle ID	com.jetpack.alpha
	Commit	f7098f8
	Installation URL	349m4cpgu6j80

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.