Flying to the UK one day before ID expiration as German citizen

I am a German citizen working and living in the UK.
I will be going on a trip to visit my family in Germany in December and will return to the UK in January.
The flight is one day before the expiration of my German National ID card.
My ID card still says I live in Germany even though I officially deregistered from my last residence in Germany.

I read online that to travel my ID just needs to be valid on the day of entering the country but I also read other information that I might run into problems.
gov.uk Says my document needs to be valid for the whole stay, I have no idea how that relates to me.

I have an appointment booked at the German embassy for a new ID but I couldn't get an appointment before February (thanks Brexit).
I will also try to get a new ID in Germany instead but it will most likely not be ready before my departure.

I am concerned I might run into problems which would delay my return to the UK by a lot so I'd rather cancel my tickets instead of having to deal with that.

I'd be grateful if someone could please shed some light on what the rules are in this case?