Does Ecobee require an app and account to be activated, or is it something that HomeKit just detects on the LAN?
Of course the app stops working, but that’s expected from a WiFi product.
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.)