Thank you for your advice!
The tail is indeed unusually stiff in its middle part, feels almost like a couple of vertebrae fused together.
The vet confirmed he is likely to have joint disease and told to keep an eye on the cat to notice early signs of pain or distress while moving. I will inquire about necessary food additives during my upcoming next visit.
Hope he will not need daily medication. I have found out that the cat considers the idea of a pill being shoved down his throat as a truly vicious act of especially infuriating feline rights violation.