I did a much easier solution for my airconditioner (also in Tokyo so everything OP said applies): I bought a broadlink rm mini3 (IR emitter) for <$30 and hooked it up to homebridge using homebridge-broadlink-rm [0].
Then went ahead and recorded all signals my aircon remote could send and put it in an excel sheet for safe-keeping. Next, plugged the IR codes into the homebridge plugin, put the small device in line-of-sight with the aircon and tadaaa, my old ghetto aircon is now smart.
For getting the temperature of the room, I use other devices (a netatmo weather station) and used their API to pull the current degrees into a textfile on the server that is getting fed into the airconditioner plugin.
Bonuspoint: I use the same IR emitter to control my TV. I just have to make sure it's in a place that is in line-of-sight with both my TV and aircon, but given how small apartments here are - that was not a problem. The plugin has a functionality to frequently ping an IP for checking if something is turned on, so I use that to determine whether my TV is on/off.