I've had this issue on mine for the fresh air flap getting stuck, along with the drivers lower footwell flap actuator.
I was able to replace the drivers foot well actuator quite easy. under the centre console an side trim, 10-20min job.
the recirculation one is a bit more of a pain. and needs the glove box out, radio unit, and cabin air filter out to see it. possible the blower motor? Didn't actually replace actuator for one this as couldn't find out how to. I only found guides for Left hand drives, but I was able to get it un stuck and reworking again, by dropping the glove box and all other stuff and taking the cabin filter.
closest
video thing I could find was for a Left hand drive VW Jetta MkV I know its old. I couldn't find any
video's for a right hand drive car, not the same i know but its enough to give you an idea.
AC recirculatory motor flap
make sure you do the flap recalibration after its done, this was about 1hr-2hrs all in.
Edit/ Apparently you should be able to access the recirc flap motor from the engine bay under the skuttle panel, but it does mean removing the wipers, and all that trim, I was mid heat wave when I did it and didn't have a anywhere coved to try it so chose to go try via the glove box
just found this one for a Gold MK5 that i'd used as well
Golf Mk 5