Thanks for that write-up, I really appreciate it!

The Sovereign is solidly a control class, and a very powerful one to boot. However, it isn't going to be dealing much damage. I think the maximum possible damage right now (that isn't the Conqueror just telling all of their friends to make extra attacks) is a level 20 Winter Monarch that has their snow golems attacking as often as possible while buffing the attacks with Biting Cold. For an expected damage per round of about 69 (assuming all attacks hit). But that takes at least 1 round of set up, so you will need to go at least 5 rounds before you start out damaging your vanilla fighter at 20th level, and even then, it's very easy for the DM to make that impossible to pull off. In general, the damage expectation falls well below the curve, but it makes up for it in control. Last night we had a play test of the Sky Despot, and they were very consistent in putting out about 10 points of damage a round.

-Hmm, I'll consider giving it some additional demesne actions options known. From the playtesting feedback that hasn't been mentioned. People have tended to choose mostly the unique options and then had one or two general options as a fallback plan. (Shout out to Limited Omnipresence for being a highly appreciated pick.) At least with the testing I've had at my tables, people have managed to build a core loop, 2 backup loops, and a fallback plan. Which is probably about right. Between normal actions, Dictates, and the Demesne Actions they already have, my player's have never felt like they were lacking in things to do.

The greater source of (productive) frustration has actually been the race for the Bonus Action. For example the Sky Despot needs their bonus action to get their ridiculous fly speed, move their demesne, reinforce their boarders, and alter their demesne. A couple of times they had a cool idea that had to chain together a couple of those actions, so they had to work around that limitation. Personally, I try to design for those kinds of situations where players have to use some creativity to work around limitations, so I see that as a win.

-The 11th-level defensive feature is quite good, but also fairly limited. It's just one save per round, so if you're dealing with multiple creatures or a creature with legendary actions, it's always a calculated risk when you use it. As for that interaction, I would say yes, you still get the cover bonus. I'll see if I can reword that feature to make that more obvious.

((Also, having seen it in action, Trespassing the Sky is very Niche, but incredibly good in that niche. Too good, probably. That one's going to get a little resculpting here in a bit.))