Another approach to this is the PAC-WHS01WF-E, which lets you plug WiFi directly into the Mitsubishi indoor unit. You then use Kumo Cloud to control the HVAC via your phone.
Here’s a thread about attempting a ST integration for Kumo Cloud; no real progress: Kumo Cloud (Mitsubishi Electric Heat/Air)
And I’m interested in the ESP8266 approach mentioned later in that thread.