Is your unit one of the ubiquitous Midea rebadges? Or at least one where the remote does 'follow me' type periodic, remote temp reporting?
If so, you're right, the easiest way is to build/buy an IR blaster module for a microcontroller (ESP32 if you want wifi) and connect a temperature sensor. HA/EspHome is overkill for this, but can be useful for the large catalog of pre built integrations. Most of them are built using/on IR libraries for 'Arduino' anyway, so you can easily roll your own with a half dozen lines of C++.
Mapping out your own PID correction algorithm (esp says the room is 72 F when it's really 70 F to get it to cool sooner), but usually just having the remote room temp sensor near where you'd be sitting instead of near the ceiling or in the return air stream gets you close enough.
If so, you're right, the easiest way is to build/buy an IR blaster module for a microcontroller (ESP32 if you want wifi) and connect a temperature sensor. HA/EspHome is overkill for this, but can be useful for the large catalog of pre built integrations. Most of them are built using/on IR libraries for 'Arduino' anyway, so you can easily roll your own with a half dozen lines of C++.
Mapping out your own PID correction algorithm (esp says the room is 72 F when it's really 70 F to get it to cool sooner), but usually just having the remote room temp sensor near where you'd be sitting instead of near the ceiling or in the return air stream gets you close enough.