Browser notifications work now, though.

(I get spammed by them from GitLab CI as coworkers revise their merge requests. ;)

A single-site browser and a caching proxy seems like a lot less trouble to get roughly the same results?

I'm partly playing devil's advocate, especially with the proxy bit, but also genuinely scratching my head. Those seem slim advantages. I'd want something that you really can't do in Webland…