The only thing I could think of is that perhaps you have the itch.io app running in the background and it’s making a large number of requests for some reason. If you do have the app running, try turning it off and see if it makes a difference to your on-site browsing.
Viewing post in Way too easy to get error 429 when using itch
This was happening to me a lot lately. I don't bulk download either. And also I kept seeing "a new version available" all the time on top right. I click it and it seemingly installs successfully (because no errors) but in fact, nothing happens. I think the auto-installer helper is running in the background and fetching a lot of data repeatedly. Then failing and then fetching again. I installed it manually and I think it's gone now.
I think I was stuck on 25.5.1 if I remember correctly and now upgraded to the latest (25.6.2)