same here, steamwebhelper stuck on my bottles after letting steam install its latest update yesterday. Won't launch.
Tried reinstalling the bottle, then it worked for one session - e.g. logged in, checked a game if it works (Cultic - not that it has any relevance here), then exited steam. Won't launch since then. I have a few steam bottles, all behave the same after the steam update. With some I see 2 steam icons on the dock, with some I see one. Both cases won't load up the Steam UI. The ones with 2 icons show a popup saying "steamwebhelper" not responding and offers some choices - none of those work. Is there a way to install a previous version of steam ? (guessing not, but hey)
edit: forgot to mention versions: I am on MacOS Ventura 13.4 and Crossover 22.1.1 (22.1.1.35679), MBP 14" 2021, 10 Core CPU, 16 Core GPU
Also: sometimes I get it to load up steam by toggling options like ESync, or repairing the bottle. Then it works just one time, it loads up steam, I can see my games, I can play my games... but every time after I exit steam and try launching it again, it won't load. Seems/feels like some sort of corruption happens somewhere. Or some library's entry point / memory address "moves" again :D
Either way, hope this gets fixed, and/or someone finds a workaround soon :)