You can see the list of integrations that are currently officially supported at this link:
https://www.home-assistant.io/integrations/#all
There are also a huge number of unofficial integrations in the HACS (Home Assistant Community Store). I started with Zigbee, Z-wave and Evohome and now have about 20 integrations and 4 HACS add-ons. Most run with local APIs rather than through the internet so are far more reliable than when I left SmartThings. I’ve moved Evohome to the experimental local control version that uses and RF transmitter on my Pi rather than Honeywell’s servers. This is great as it’s almost instant and doesn’t rely on an internet connection.
There is a SmartThings integration, so you can just setup Home Assistant, add this and then migrate integrations one at a time as you feel comfortable.