Hi Stefan,
Thank you very much for the details, it helps me a lot!
I see you have the attachments search enabled, but the video mime types are missing from the list. To search them, I have added their mime types to the allowed mime types list. Now, searching their stored titles or the file name, should return them in the results.
The other videos (in the total soft video gallery) seem to be within a custom stored table, not as custom post types or media attachments, so those cannot be searched and returned as results.