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Many computers users use a tools to organize one's files, like moving images to specify directory, moves music to specific directory, etc.

Imagine we build-in these tools to file manager. I imagine panel with mimetypes tree, which will be shrink to mimetypes of files present in current directory. User may select files by selecting mimetypes.

Did you check the "Search for" section in Dolphins sidebar? You can search by mime type already...

The search function can do this
https://i.imgur.com/IBwaYYh.png
The reason baloo and its predecessor back in KDE4 were created was to remove some of the need for organizing files so much.

I am sure a service menu for moving files to a location based in file type either exists, or could be created with a small bit of work if someone is interested.

or modify an old one (if needed) to make it work
https://store.kde.org/p/998258