Thanks for your report and for your screen shots; very helpful.
The category selection and search box controls are present, but hidden by the image thumbnail grid. If you look carefully just below “Show all dates” you can see the top of one control.
I found two Disable Gutenberg plugins in the Repository and decided that the plugin by Jeff Starr is the likely candidate. I installed that plugin and verified the problem. It is caused by the way the plugin creates the “Add media” popup window, which is not the same as the standard WordPress Gutenberg method and by the “Classic Editor” plugin you might consider as an alternative.
I have made a change in the MLA code to accommodate the Disable Gutenberg plugin and uploaded a new MLA Development Version dated 20210816 that contains the fix. You can find step-by-step instructions for using the Development Version in this earlier topic:
PHP Warning on media upload with Polylang
Once the Development Version is installed you can verify that the toolbar display is handled properly.
The fix will be in my next MLA version. In the interim, it would be great if you could install the Development Version and let me know if it works for you. Thanks for alerting me to this issue and for your interest in the plugin.