Are these herbaceous peonies that have been in place for several years? I noticed several of mine have larger than normal eyes but I'm not seeing stalks coming up or anything, is yours similar?

All herbaceous, NONE old. They were purchased and planted this fall, and I have a couple that were planted two falls ago (that I haven't checked on yet), so they just finished their second summer. This is what my brand new ones look like. To me they seem rather plump for November.

One in the first picture is sitting up too high.

I agree but also think the second one could be a little deeper. Light and warmth such as your area has been having will cause buds to swell. Many peonies buds will swell at this time of the year. Yours do need to be planted deeper. You should have time to dig and replant before the first snow if you hurry.

I’ll add some soil. I tend to err on too shallow rather than too deep for sure. I also scraped away dirt so the buds can be clearly seen, but even with that they are planted shallow.

In zone 5 the pink eyes should be at least 1 1/2" below the soil, no part of the roots should be visible. You'll want to resist the impulse to brush soil away to check on them as well, the eyes are easily damaged. Don't want to sacrifice next year's stems and possible flowers!