When it comes to mini splits I doubt you will have much of a choice in how you can control it. I believe they are all controlled with high voltage communicating 'proprietary' thermostats. Meaning, you use the thermostat that came with the unit. (High voltage means probably 115V, communicating means it speaks gibberish the nest won't be able to figure out. Plus, the Nest won't work with high voltage... 24v controls only)

The manufacturer's of these mini splits control everything. So when the thermostat goes out, the manufacturer is the only one in the supply chain to 'turn it on again'.

Here's a compatibility checker of sorts, but this 'for after' you have already bought the mini split. To compare what you have versus what you don't.

Nest compatibility checker

Here is a YouTube video that may be helpful: How do I Control My Mitsubishi Mini Split With WiFi?

There are three options shown including adding the interface for the Nest. The Nest option seems to be the least desirable of the three. You have to verify your HVAC company is willing to do this type of installation. They may not want to be responsible if there are problems.