Of course I was not able to notice this when I was younger. Only now at 32 and a family these measurements are starting to actually be noticeable.
If you look at the app and see that it says "better sleep" before starting the day and then notice that you had a good mood or felt better after that could be a placebo effect.
You could check that by not looking at the app until after your day is done and you have noted if you had a good mood or felt better. If the app and your day's mood still correlate then it probably is something real.
On the other hand checking if it is real risks making it no longer work, and a good mood is a good mood even if it was caused by a placebo. I'm not sure I'd check.
The placebo effect doesn't go away if you know it's a placebo: if it's worked in the past because you thought it did, it will continue to work if you think it will. https://xkcd.com/1526/
Especially if you're wondering all day if you're in a good mood or not.
It might not even be placebo! Perhaps the combination of (well rested) + (optimistic) means you have a good day, and the experiment changes those conditions enough that you get different results. Heck, you might end up having better days more often. You never know if you don't try.