Now this is a late reply, sorry about that.

When I restart the tweaker it doesn't make the taskbar narrow again, nothing happens. It has to be manually resized every single time, so I naturally just stopped using the feature and left it wide.

If I set Windows 10 scaling to 100% on both monitors it seems to preserve the width of the taskbar when switching back and forth between the monitor/tv. If the 1080p monitor is set to 100% scaling and I switch to the 4K TV's higher scaling like say 200%, then the taskbar initially preserves its low width. However, when I then switch back from the 4K TV to the 1080p monitor and Windows changes scaling from 200% to 100% that's when the taskbar is left in a large wide state, at which point it has to be manually resized again.