Is there a way to see what you sunrise/sunset times actually are?

The sunrise and sunset times are made available to legacy apps by the Weather Station app as you’ve seen - the app sends out events at your local sunrise and sunset, and then sends out events updating the times for the next day a little while after sunset.

In the ‘new’ environment other methods are used but the information is certainly available in the API. In Curl speak you can do:

curl --header "Authorization: Bearer ACCESSTOKEN" https://api.smartthings.com/services/coordinate/locations/LOCATIONID/capabilities?name=weather

and that will include:

"sunriseTimeLocal": {
  "value": "2021-02-18T07:07:48.000Z"
},
"sunsetTimeLocal": {
  "value": "2021-02-18T17:21:44.000Z"
},

I’m not suggesting that is in any way an optimal or even an approved way of accessing the information, only making clear that the information is certainly sitting there in the API for apps to use.