Hi Julia, three observations from me, based on the photos, so I may well be off track.
1. The damp patches on the drum, was that as a result of WD40 or such like to get the drum released.
2. I would expect the drum surface to be more shiny if the brakes were operating correctly. Think of a used railway line vs unused railway line.
3. On second picture there does appear to be a damp area to the right of the left hand dust cover of the brake cylinder. If it is not WD40 or similar, it does suggest you have a small leak on the brake cylinder.
Apologies if teaching someone to suck eggs, Brakes are just too important not to comment.
If you are taking the brake shoes off, I would just give the back plate a good clean and smear a tiny amount of copper grease where the brake shoes will rub the back plate.
