I wish Destiny 2 had a "turn off friends coming online" notification on Xbox as well.

Not available on consoles for some dumb reason. If you have cross-save enabled and can play on pc, log in on your computer, go to settings, social and scroll all the way to the bottom. There will be a blank option, click the right arrow once and then log out. Log back in on your ps5 and boom, no more "so and so is online" messages. It's the only workaround other than turning off text chat completely.

From home screen :- Settings - Scroll down to [b]Notifications[/b]. Notifications - Scroll down to [b]When Friends Go Online[/b]. When Friends Go Online - Turn off [b]Show Pop-Ups[/b]. Or you can use the other toggles to filter the activities that will allow notifications. You can also select individual friends to send a notification. Note - from Notifications top level menu you can just turn off all pop-ups. HTH