I’ve given this a lot of thought, and I think that to improve the UX of filters on mobile screens, they would need to be implemented like a slide out panel. However, if implemented this way, it would likely need to overlay the table and not retain its state. (Of course, there may be other possible solutions for this.)

Currently, the admin can have two side panels (app select and filter), but I feel it would be better and a more definite improvement to provide side panels in one place only, using a tabbed interface, rather than offering them in multiple locations.

While there are realistic solutions, I believe that even a slight structural improvement could lead to a much greater enhancement. However, such work would be significant and feels closer to a modernization effort. I feel the admin interface needs modernization, and that it should be improved overall through extensive discussion and coordinated efforts.