Various websites suck in one browser or the other or simply don't work in more than one single browser. We're not that far away from the days when Internet Explorer (IE) was the only thing that loaded a site (often for something work-related... groan)
That said, if you need Chrom(e/ium) and want a non-data-sucking version, I think Ungoogled Chromium is your best bet currently.
For the Firefox side of things, there are already several forks that aim to do things differently/better. Floorp is one I see recommended regularly. There seem to be a larger number of Firefox forks focusing on security/privacy than Google forks, but this is the most well-regarded from my research.
Simultaneous post-enshittification from both Chrome/Chromium and Firefox is probably (hopefully) leading towards more active development/contribution to these (and other) forks!
Running Android 14 and somewhat disagree. I have had 1-2 games running in the background after "exiting"/"quitting" the game and dropped from 80-90% battery to 30% in less than 2 hours. (GPS and Bluetooth both disabled). Battery dropped as though I was actively playing with the screen on during that time.
Killing apps has helped me with this issue, in general. However, for the offending game, setting "app battery usage" (specific to Android, not sure of iOS equivalent, if any) has helped better for this issue. Seems a lot of games are trying to load unmecessary stuff and/or sell usage data, despite exiting the game...