Alpine works great for the desktop and I’m using it myself for my lower end machine.
Working without glibc and with some strangly named packages is sometimes tricky, but so far I have been able to do anything I’d wanted!
If it can help you in your journey, here is my personal configuration for Alpine, with WMs and DEs on their own branches. Only the ‘suckless’ (DWM) and ‘xfce’ are working properly so far: https://gitlab.com/sunoc/als/-/tree/suckless?ref_type=heads
I had similar unexpected behavior with a closed Telegram tab. Feels weird and a bit worrying that stuff is allowed to run in the background like that.