I'm building a niche social media PWA (eschewing native apps to save time), and use browser push notifications to let my users know when someone has DM'ed them.
I prefer running Slack in the browser, and I need to receive message notifications.
Push notifications aren't any less useful to have in browsers than in native apps.
Though I would like to see the prompt locked behind "add to home screen".
The thing is, many non-technical users don't even know where or how notifications really show, much less how to edit/remove them.
At one previous job, that supported vehicle registration for county clerks, there were enough situations where multiple users would "work" on the same vehicle registration that we had to let users know if some other user updated that particular record - rather than fail/error if that user presses submit "too late".
Even to use this theoretically, though, I'd want the strict ability to control who can even send me a direct message. As it stands, the only thing I currently allow push notifications for are SMS and Signal, but the SMS texts are still overwhelming election spam from people who aren't even trying to spam me but have the wrong number for my mother or grandmother and bulk property buyers who claim they want to buy one of my houses. So I hope you plan to enable user-controllable proactive origin filtering (not after the fact user-by-user blocking).
Consider food delivery services (from the reastaurants). We actively order food directly from the reastaurant where possible, because Uber Eats charge more for the food and still charge "service" fees + delivery.
I've just checked, and I have 7 (including Uber Eats) food and grocery delivery apps.
It would be my preference if I dealt with a PWA instead of having to install many apps with varying quality. A notification of the status of my order is useful, and with the grocery apps, sometimes an item that I've ordered is out of stock, and I have a small window to take some action (if I hadn't chosen one when ordering).
Browsers should've really made it an user-initiated action. Something more akin to adding a site to your browser's bookmarks than what we have currently.
The other big positive is that the closer PWAs are to native apps in functionality, the less of a stranglehold Apple and Google will have over app distribution.
Push notifs in a PWA get us about 90% of the functionality of a native app on Android and (finally) iOS.