Change wp_make_content_images_responsive to wp_filter_content_tags

[johnstonphilip]

Fixes #21514

Description

Swapped the call to wp_make_content_images_responsive for Template Parts to wp_filter_content_tags, in-line with the change to the_content in WordPress Core here:
https://core.trac.wordpress.org/changeset/47554

How has this been tested?

1. Ensure you are on WordPress trunk
2. Use a Block Based Theme like https://github.com/WordPress/theme-experiments/tree/master/parisienne
3. Notice you see a notice that wp_make_content_images_responsive is deprecated since 5.5.0.
4. Switch to branch try/replace_wp_make_content_images_responsive
5. Notice the notice is now gone.

Types of changes

Bug fix

Checklist:

• My code is tested.
• My code follows the WordPress code style.
• My code follows the accessibility standards.
• My code has proper inline documentation.
• I've included developer documentation if appropriate.
• I've updated all React Native files affected by any refactorings/renamings in this PR.

[joemcgill]

This change looks good to me for now. Thanks!