Hi everyone! After a bit of testing I did in the meantime I can say everything is fine. Almost everything.
Saving (or better say copying of) images from Files app or some different app to Photos app works ok. However, images are saved and placed to a position there according to their creation date, thus they are not simply added to the end of the list and with current date, but are kept as they originally were, timestamp including. So, one can most easily and quickly find them through the Recently Saved utility (I didn’t notice it earlier). But, I noticed, that Duplicates utility in Photos, when and if available, doesn’t refresh its contents in real time, therefore it is rather unreliable.
I also noticed, that - for example - (only) certain video clips from the Telegram app chats don’t really(?) get saved to Photos despite original app (i.e. Telegram) saying otherwise (‘Saved’ or ‘Saved to Photos’ at the end). I couldn’t find them in there.
Anyway, I think admins can close my case now. Thank you to everyone for your help, and all well in this newest year❗️🙂