So. Uhm. I made the thing. The feature was of course coded by Leafo, but if there is a doodad to activate it besides typing or copy pasting it, I have missed it so far.
It is an unpacked chrome extension and adds a button and a box to use the feature. You still have to type the tag, but it will stay there until you clear it.
https://redonihunter.itch.io/itch-browse-tag-exclude