From my experience... and I can't speak for the whole of the US.
Schools went back carefully, with masks, distancing, and extra ventilation. Cases in schools were very low. There wasn't a huge hurry to get schools back because hybrid/online learning went well.
Ditto universities.
Reopening gradually seemed to help. In my state we reopened stage by stage, county by county. We didn't open bars till very last, because pissed people aren't going to socially distance.
Everyone over 12 who wants a vaccine has had the chance to get both shots. Today I drove past a brewery that had a vaccination clinic in it, the supermarket was offering walk-in vaccinations, you can call up your GP and get a vaccination on the spot.
The UK is seeing a surge, but that's partly due to having recently reopened. Most of the US has only had limited restrictions for the last year, so we've already gone through those post-lockdown surges.
We've had very easy access to testing - no strict rules about only being allowed to test if you have 3 particular symptoms. If you're at school and you have symptoms you just go to the school nurse and get a test. We do things like mass testing after school vacations.
We've been offering no-symptom tests for ages. Mostly we use the Abbot BinaxNow tests which seem to be fairly reliable and give a result in 15 minutes. I've tested hundreds of people using them.
We had a track and trace system in place but no longer require it. It's there if we need it again.
I really do think the UK will be there soon. Just need to get as many people as possible double vaxxed. Life will be back to normal.