We've done the DP twice - it's our favorite thing to splurge on and the only dessert party we've ever done multiple times. Both times it was myself and one other adult. We lined up about an hour prior, but just because I am super short so high top was a must. The first trip we were sat with another couple - ironically a couple we had been chatting with in line, so that was kind of fun. The second time, we had our own table.
I totally get your anxiety being sat with others! It wasn't bad at all! I will say, we've only had one negative experience at a DP, and that was for illuminations in Epcot. DH and I were sat with a mom and 3 kids who clearly thought adults without kids had no place there. We just ended up mostly ignoring her, haha.
Disneyland has never made it feel awkward for us!
On another note - anyone think Disney is going to take advantage of the re-opening and pump out some new merch? My old hoodie from 2016 is getting kind of sad and there wasn't a lot to find for adults last year!
Edited to add -
@ash-n-brensmom that's our date as well!! See you there!!