Start Simple is my suggestion. Home Assistant supports a huge range of integrations. Personally I am using Broadlink RM4 Mini IR blasters. One in each room.

Start Simple is my suggestion. Home Assistant supports a huge range of integrations. Personally I am using Broadlink RM4 Mini IR blasters. One in each room. They get added to Home Assistant as devices. Then I use one of the climate add-ons that can send IR commands via the Broadlinks.