So I'm reading this in Feb 2023, please tell me there was a solution
I had the exact same problem. Once I logged in with my samsung account on the wearable app on my phone it started working.
Check if you are logged in before trying to download
I had a pixel 6 and now a pixel 6 pro. And I've never been able to download watch games from the Samsung wear app to my galaxy watch 4. I just get the "There was a problem connecting to the network. Try again later"
But it seems to be common for this error message to appear for those who are not using a Samsung phone with their Samsung watch! Maybe Samsung are trying to push people to use Samsung smart phones instead of other manufacturers phones!