Slax (https://www.slax.org/) runs entirely off of a USB stick. There's other options that have been around for awhile aimed at simple experiences for older and weak hardware.
Back in the netbook era, there were quite a few that tried to be internet browser focused like peppermint OS, though I don't know how well any of them faired with the rise of chromeos.
I still love Peppermint OS and have used it on several low end boxes.
It also didn't try to be internet browser focused, it just gave you easy ability to make the OS browser focused. Out of the box, it was like a better Lubuntu. You had the opportunity to chose what web based apps/services you would add.