What version of Android is that? Have you tried swiping away the notification?
Swipe it away is okay? Or will this disable the notification (function) too?
It's a Samsung S23 with the latest available update:

I think it depends. On official Google devices it will hide the notification, but will still show the app as "running", which means it is in the right foreground mode.
The white dot is really annoying and ugly (and I think it will burn in with time...).
I see also no option to hide it on my phone: