Some quick feedback

Hey DeBAAT

Here is some feedback I have from a quick look through your plugin based on my area of expertise – UI and design.

Other similar plugins https://wordpress.org/plugins/enhanced-media-library/
https://wordpress.org/plugins/wp-media-library-categories/

Search:
https://wordpress.org/plugins/search.php?q=WP+Media+Category+Management

Test them out and see how the various plugins do things compared to your own plugin.

Sidebar item: WP MCM – What about just using MCM here as well?

View all categories. Nice that you have included a () showing how many media items are associated with each category.

What about iIncluding a link to settings beside Activate-Edit-Delete-Then Settings

What about changing the setup?
Have one settings screen with two tabs. Then place the MCM directly into the WP Settings section.

Looks good.

I also tested the plugin using the P3 plugin for speed and it is not taking a lot of resources.

https://wordpress.org/plugins/wp-media-category-management/