I know they used to be Home Assistant capable but required an API key which they will no longer give out. Seems like no fully local control to me. I believe my app stops working when the Internet goes out but it's been a bit.
Oh really? Weird. I did need to do some developer API key thing to get mine in HA, and it's awesome. All sensors and controls work great[1].
Since it's Homekit compatible though, you can go that route. HA easily discovers anything HK compatible as soon as you connect it to your network. So you connect Ecobee to HA with the HomeKit protocol in lieu of connecting it with Apple's stuff.
[1] ...and anything's better than the asinine on-device UI that Ecobee "updated" to a couple years ago (ask yourself: what would a foolish inexperienced "uX dEsIgNeR" do to ruin a plain old thermostat UI? It's that.)
Of course the app stops working, but that’s expected from a WiFi product.