Hey Karina,
I believe there is no problem with my stability and speed of my mobile network. I put my sim card to my old phone Samsung Galaxy note 9 where I started a hotspot and the Application worked without problems, just difference was that my hotspot from iPhone is recognized as a Personal hotspot and my note 9 was recognized as a normal wifi network. So I believe that the issue is somewhere between the Photos application or the feature called "Personal Hotspot".
Here is something interesting - Photos show last time when was synced and it is yesterday at about 22:30 when I was connected to a WiFi, not my Personal Hotspot. I am using it a whole day and there is no change, seems that Photos does not want to even try to Update and Sync while My hotspot is connected.
I have tried all workarounds I found on the internet, full battery, connected to a charger, and so on and so on, and so far nothing helped.
Martin