@Beth21 Short answer is, I think that sounds normal. I don’t think your Switch is broken/defective.
It’s the quirk of the Switch that I and most everyone has seen since Switch launch in 2017. Needing to re-pair the controllers sometimes happens. Usually happens with third party games, I think – I could be wrong. I get the issue with Rocket League sometimes, and it’s not the only game.
When you go to boot up some games, the game takes over, and it’s like the console forgot you already paired the joycons/pro controller. But after you’ve re-paired the controller, you’re good to go for the rest of the time playing that game session. I don’t think the issue has ever raffected playing a game, since it only seems to occur before you start playing a game.
And yes, the message tells you to press a certain button, but it seems like it doesn’t matter which button you press. I think I just hit B to back out, even though the prompt says L + R.
Edit: Sometimes, when playing handheld, the right joycon may un-pair, but it’s only when starting the game, once it’s re-paired, it plays fine until I’m done playing. (this issue was worse with launch consoles, and is less a problem with consoles sold after 2018-ish – they altered the internal antenna.)