Take a look at zigbee2mqtt this is what I use to add any of my ZigBee devices to home assistant. You may find there is more frequent reporting/polling with this so you have more updated information in your home assistant instance.
ZigBee is the way to go IMO for the most “local control”. Your thermostat is probably pretty good and would not need replacing for a long time.
For automation of your thermostat and other items in the house you will need to setup your own automations that work for you. Home assistant won’t do this for you automatically like other 3rd party thermostats that “learn” your patterns.
Home assistant is pretty powerful in what you can do with automation as it’s allows you to use other sensors around the house, even poll outside stats like weather. So in theory you can set automations that turn off your heathing if your phone or all phones have left the house. You can set automations that turn on the heathing when the outside temperature reaches a certain temperature and the house temperature drops to a certain point.