I think I figured it out last night, maybe. I now show 4 more recordings needed! I'm not sure if it's just a fluke though, but I will update if all 5 recordings go through...
When you're on the screen in your screenshot for the sleep schedule, there is an option there that says "Edit sleep schedule in health" ... inside that option, there is a toggle near the top that says "Use Schedule for Sleep Focus". Make sure that is on. I was helping a friend set their watch up last night for sleep tracking, and I realized that option by default seems to be off. If yours is already on, that's fine, keep reading... mine was too... but...
This is what led me to check mine, and then I had a light bulb moment. Eureeka! My sleep schedule was on, and sleep focus was set to come on, but I had set it a bit too early and when it came on automatically previously, I was shutting it off until I went to bed, then turning it back on manually. Turns out, I don't think that works. I think sleep focus has to be on automatically for it to track the temperature. I don't know why, as this seems like a bit of a design flaw to me - I think it should be able to be manually enabled and still work, but I don't think it does. So last night, I set my schedule back to an appropriate time that I knew I would absolutely be in bed, and I did not turn it off. I let it stay on and do its thing.
This morning, I checked vitals on the watch, and lo and behold, it worked! I hope this helps you as well. It seems like such a silly little thing, but I didn't think it mattered as long as sleep focus was on, and turns out, it does matter. @@ Good luck! Please update if this worked for you too. :)