HVAC system questions: smart vents and dumb thermostat (brain in homeassistant)

Hi guys
We recently installed a new floor and it seems that this unbalanced the HVAC system to a degree. The top floor was warmer in summer and colder in winter than the basement for obvious reasons . Now with a new floor the differences between the two increased and I am looking for solutions.
I have only one thermostat and a HVAC system with two supply plenums similar with the below oneBasic-Duct-Layout1

The only temperature sensor that the thermostat works with is its own and that is placed in a bad spot (a hallway) .
I am looking for two things:
-a HVAC thermostat or controller that is as dumb as it turns on and off via wifi ,with the logic being hosted by something like HomeAssistant. HA will also read additional temperature sensors that I would add to the system and instruct the HVAC controller on when to turn on and off
-a solution to dynamically adjust the airflows in the system for a better distribution of the temperatures. The heat situation is OK over the winter although not ideal. However during the warm season I very often find the basement dead cold while the main floor is still relatively uncomfortable warmer and it needs the AC to run longer. (this is forced air HVAC). The new floor was installed with subfloor and that obviously decreased the air circulation between the two levels even more. Even if the return duct would take some of the cold air from the basement and send it back into the system and maybe help with the situation on the main floor it is not enough.
So I am considering some automated solution that would either control the vents or the two supply plenums (work with one at a time instead of both fully open at the same time)
What hardware can be used to address my issues ?