Identify this tarantula

Hello arachnid lovers of the SDMB. I just discovered this tarantula-like spider (not scary - it is quite small) in the staircase of my building. I was hoping someone here could tell me what species of spider it is. It looks very small, but those wires aren’t as thin as you would suspect. I estimate its length to 4-5 cms.
I am kind of hoping that it is one of the few tarantulas (if it is a tarantula) native to Denmark, as I have never seen any of those.
Also - what is it doing in the middle of Copenhagen in the middle of (a quite warm) winter?

The ‘stance’ and the ‘ends’ of the legs look wrong for any tarantula I have ever seen.

“T” stand different than that and the ends of their legs are more blunt or rounded.

YMMV

Not a bug guy, just an country boy.