I've never seen that one but the APS peony database has it listed as a magenta Japanese peony. Those typically do look like a single but there's a cluster of very short, thin petals or really prominent stamens. The only peony that I've personally seen that truly looks red to me is Red Charm but I haven't bought red peonies until the last couple of years....Buckeye Belle blooms a dark crimson here. Soil conditions will make the colors vary a bit, especially on the more dramatically colored blooms, so it could be more of a dark red for you, not sure.

I saw the Red Charm bloom at the University of Michigan peony garden in Ann Arbor, MI. They have a huge assortment of historic peonies, don't know how close you are but it's worth a drive! They also have quite a few pictures of their peonies on their website.

Another thing to consider when planting peonies close together is their bloom time. If you have 2 that will clash but the bloom times are different, problem solved!

I've not seen that one either. I have Buckeye Belle, it is a very handsome dark, dark red. Not pillarbox, more wine, but not purple. It's very healthy and vigorous. Be warned, when you cut it down in the autumn, after the foliage dies, don't pull on the stalks, becase next years buds are attached. However, if you do accidentally pull one up, (my nieces were helping!) it can either be reburied or potted up and will likely go on to form a new plant. I also have Red Charm, and agree that it is closest to true red of all the 'red' peonies I have.

I have a succession of dark red flowers in that area, hence
wanting to stay with the same range.

Thanks to both of you for your verbal description of the
colors. It’s a challenge, describing a color with mere words. I’m not sure what
color crimson is, just have heard the name many times without thinking about
whether it meant a cool red (purple overtones) or a warm red (orange overtones).
A rich red with a slight magenta or purple cast? Wine or dark red for the
Buckeye Belle should work in this location.

I had asked the vendor for red, so if it’s magenta, I’m
disappointed. I bought it at a garden fair, so it’s not like I can return it.
Nothing wrong with magenta in itself, it just means I will have to find a
completely different place for this one. You know how colors are described in
grower-speak as being different from what they actually are, like “blue” most
often is really purple. So although she describes it as “red” on her website,
everything I found last night indicates it’s in the deep pink/maroon/raspberry range.
Sigh….

Bloom time of “midseason” will probably overlap with Buckeye
Belle, described as “early mid season”.