I can't give you any ST specific advice, but I figure I can share my Hubitat to HA experience as there may be some tidbits that could be useful for you.
The biggest bit of advice I can give you is around the other people in your house and ensuring their experience is similar or better than what it was. I did this two ways: First, as mentioned in the other comment, link ST to HA and slowly transitions devices to native HA (I have z-wave and thread/zigbee radio). Second, I bought two low-end Android tablets, installed the native HA app, and created meaningful dashboards. The UI change alone between Hubitat and HA was a huge win. Not sure what ST's UI is like, but Hubitat blows chunks.
A lot of your transition is going to come down to how the other people in your household interact with your smart devices. If you use Google or Alexa, then make sure to keep similar names of devices or groups as you move them over to HA. If you primarily use the mobile app, take the time to walk everyone else through the UI and make meaningful, mobile friendly dashboards. If you rely mostly on automations through sensors, make sure you set up the automations in HA as a part of transitioning devices.
Take your time, I rushed a few devices and got some constructive feedback from the wife about it. Little did she know I had already transferred 50% of the devices.
Learn the YAML configuration patterns and capabilities through templating for automations. The UI does an "OK-ish" job, but you can really unlock the power of HA if you take a bit to learn how to set up automations using templates and calling the back end services. Learning this took HA from "slightly better" to "way better" than Hubitat.
Enable Home Assistant Community Store, commonly referred to as HACS, to get access to a lot of open-source tools and add-ons for HA. Development is very active in the community for HA and there are a lot of fantastic integrations and UI upgrades.
I can't stress the "take your time" part enough. It's been tough for me because I get distracted easily and since this impacts the productivity of my family I wanted to make it the best for them. It's been about 6 months since I've started the transition and I finally just powered down my Hubitat yesterday. The family is enjoying the automations and dashboards much better than anything Hubitat provided, but it definitely took easing them into it.
Hope you enjoy and feel free to let me know if you have questions - I'm still a beginner at it, but have really liked the platform so far.