What does this error mean “stop vehicle, shift to P, leave engine running” error?

That error usually means that there is a problem in the charging system. That could be a bad battery, bad alternator, bad regulator or a problem in the control system. To find the actual problem you will want a scan tool to read the code(s) that should be stored relating to the charging system. That is because of the way that charging system operates using the various modules. You can start with a simple alternator test using a meter.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

However, the scan tool will be the next step.

Hi there! Thanks for your help, very much appreciated. I followed the instructions and the link that you sent me, as well as elsewhere. So, when the car was off, the battery was at 12.6 V, when I started the car, it jumped up to 14.8 V. When I ran the air conditioning, radio, everything else, it didn’t change at all. So, it all appears to check out. I also used an ODBC2 scanner, and no codes came up. Any thoughts?

Okay, that sounds like the alternator and its controls are working. Codes will depend on the scan tool, some work well with Mercedes and others don't seem to speak German all that well. I have a nice Snap-On that can get some data from them and a Launch that can do everything the factory tool can. Which scanner do you have?
Next step, take it out and drive it to get it warmed up and see if you can get that error message, test it as you did before, see if things changed because it warmed up. A bad connection could change from heat or moisture. Have you noticed any pattern to the error, like it seems to do it while it's raining, or a couple days after rain? Or it does it more on hot days?

Actually, I ended up taking it to an independent shop near my house. They tested the whole charging system; everything came back good. The guy who tested is fairly experienced with Mercedes, and said the car sometimes throws this error when the auxiliary battery is going out. So, I’m going to find that online and they said they’d replace it for a reasonable fee. So, thank you for your help! I think I’m good from here!

Yes, the aux 48-volt battery could do that if it is failing or its converter is going bad. These are the OE instructions for its replacement. The battery first and the converter that also gets removed second. Depending on the scan tool you might be able to read the voltage and the converter state using it, but many cannot read that data. Please let us know what happens.