Did this solve it?
I've got a similar problem on my gla 220d 2016 - fault codes for exhaust flap actuator and limp mode. I removed the actuator and the flap itself is free to move so not seized. I also have access to a working star/ xentry diagnostics so I can test via that to move the flap to different position, however when trying to test a week or so ago, xentry says the external temp needs to be 10C or above or it doesn't let the test run (assume due to the possibility of the flap being frozen or blocked by ice below this temp). The issue has only now reappeared during the warmer weather, so I am guessing the flap is also not used when the ambient is below 10C.
So thinking of getting a new actuator to try - they seem to be around £200. I see I can 'teach' the new one in star.