Debian can be pretty light/small on a clean install and xfce should run fine on 2gb. Although the biggest thing is gonna be if the laptop has fast storage or not. Since its a celeron it might not be upgradeable, and if it doesnt already have an SSD any desktop will feel slow
Personally if I really wanted to squeeze all the performance I could for web browsing I’d go with minimal Debian and RiverWM but thats a bit more involved
In a similar vein I really miss rainmeter, now I’ve gone down the deep rabbit hole of EWW and AGS but rainmeter was way easier
My solution has entirely just been to own less things and designated spots for every item. The main problem is forcing myself not to get cool things I will never actually use