I guess I’ve never clicked on the share button to republish any changes, but I may have to try to see if it makes a difference. Everything should be published automatically and almost immediately, but I have had some small changes take awhile, even with force closing and reopening the app on my phone. You can’t rely on a user to force close and reopen, but like I said, the changes do migrate eventually. I think if there is enough changes to the app that cause some internal conflict, then the app will restart and auto sign in again.
I look at it this way. It can be weeks, months, or years for someone to update an app store app, whereas it may only be hours or days for a PWA to update on all user devices. You are alway at the mercy of the user to some level.