Plugged Drain

If you're super picky about never putting any kind of dish washing water, grease, etc. down sink drain there shouldn't be a clog. If you use it be real careful with the Draino and really rinse well after. I keep a wire drain screen in all sinks to prevent anyone from inadvertently dropping something down the drain. When we were testing things at our son's house where we bought the camper water came up in the shower pan too. Duh, we didn't read the little note previous owners left that said to always open the drain cap below the black water gate valve or it would back up.....no on board grey water tank! LOL live and learn. Blue boy tank a constant companion now as no space to add a grey tank on our old unit.

Water coming up shower my first thought is our gray tank is full.
Only done it once. Id start with something a bit less intrusive like a plunger in shower, generally last in line before holding tank (towel over kitchen drains). Ideally hose connect and at dump station.
Does it gradually drain?

For the best and safest drain cleaner is Vinegar and Baking Soda non toxic, safe and works better than any drain cleaner I have ever used.

Been using it for years

That usually happens when the holding tank is full. Any chance on that being the case?

simple thought. did you open the gray water? you should not have a plugged drain.

Try using a snake if possible.
I assume you drained the tank.