That would be “the HA way” to go about it. But this assumes having ESPHome, perhaps MQTT, an HA instance, etc.
Now, I am not sure what you would do with just a Wi-Fi dongle from the mfr. (even if you could find one). Just use their app? But this illustrates (one of the many) problem(s) with counting on the mfr. You are kind of tied in and limited to whatever they are offering.
If you want to get away from that kind of thing though, HA (and the linked thread) could be the way. Of course more setup than needed just to run a single air conditioner. But perhaps worth it if you have bigger ideas of more things to integrate (as we all know, one device is just the start!).