Can Home Assistant help my heating problem?

I could possibly write 2000 words describing my problem so I’ll try to keep it as brief as possible! I’m lost with the flood of options seemingly available.

My case scenario… I live alone, I’m sat in an upstairs bedroom playing on the computer and the room is about 15c. I’m cold. If I go downstairs to the room my heating thermostat is it’s 21c (it’s just naturally hotter downstairs, no idea why!). To heat the room I’m sat in I have to turn the thermostat up to 24-26c, the boiler will turn on and my upstairs radiator will kick out some heat. I’m no longer cold. My problem is that downstairs room is now 24-26c.

So, I’ve been looking into how ‘smart’ heating might help. There’s so many options I’m bamboozled.

All my rooms have a TRV except the room the thermostat is located… I think my thermostat has a min temp of 8c so it’s setup that way to prevent the house from freezing if I were to vacate for the entire winter. It means I can keep every room at a chosen temp except the thermostat room. That has to turn into an oven just so I can heat whichever room I’m sat in.

Assuming I add TRVs (‘smart’ ones) to the radiators in the room my thermostat is located, is it possible to replace my thermostat with something which will allow me to heat each room to a chosen temp?

I’m posting on these forums because I also have a server at home running docker (podman, actually) containers which are accessible remotely (cloudlfared).

I’m also a bit lost with which thermostats and TRVs are compatible with HA. I hate unused features so if I were to do an upgrade I’d want the most basic thermostat possible which can simply turn the boiler on.

I’m in the UK, if it matters.

Thank you for any help/advice