Each time I get a permissions request, and disable one or more, it asks about them again on further launches, although sometimes you get a 'don't ask again' option as well.
An app will usually run if you deny the notification request on first launch, but will nag about it each time you open it. It's treated a bit differently than simply turning notifications OFF in settings--Apps--App name.
A more modern issue I deal with is 'this app has been closed because it has a bug [ok][clear cache]'. I find that happens a lot on One UI after Android 13, and so far my only workaround has been to either live without the app in question or disable battery optimization in settings. This is very different from '[app name] has stopped/keeps stopping'
There are so many things that modern Android does that it makes my head spin and long for the simple days of Android 2.3. Today, we get pop-ups (screen overlays), toasts (little bar at the bottom that merely annoys me) bubble notifications (similar to iOS) and icons that clutter the status bar (a problem with Android as a whole, since the beginning, never have liked it).
For example, a way to fully turn off OTA updates is by disabling the screen overlay permission to Software Update and FOTA Updates and anything with the word 'update'. That has completely disabled my phone's ability to interrupt my flow by deciding at the most inopportune time to say 'hey! a new update is available!' hoping you hit the wrong button.