Can’t really make a checklist for you unless I was in the rental space – too many variables. I had a checklist of our rental for the first 3 or 4 times, but by then it had become a rote thing.
My checklist wouldn’t help because it includes things like “Dust louvres in bath and closet doors weekly” and “Make sure pool towels did not get put away wet” – things I’m pretty sure won’t be in an Edinburgh flat!