Da-20 monkey
... Does concorde have real trim tabs?...
No, there were no trim tabs on Concorde.
...is it just an artificial feel unit that changes the neutral point in the stick?...
Yes, just so.
Concorde had conventional trim controls (electric trim in pitch, manual in roll and yaw), but operating a trim control merely changed the artificial feel datum position and thus the neutral position of the flying controls.
The electric pitch trim not only operated automatically whenever an autopilot was engaged, but could and would also operate automatically in manual flight, independently of any pilot input, to provide pitch stability corrections in various situations.
Best Regards
Bellerophon