You say "these". Is that one peony or several? Looks like one but I would rather ask. Also how large of a root did you plant and how deep?

There are 14 in all. I planted the root about three years ago. It was from Tractor Supply and I had no experience with peonies. I cannot remember how deep. All in all they do look healthy. I visited a friend yesterday that has two that were acquired when her mother passed away. They were flowering, zone 7, and a true mature peony and deep in green color. These are planted in soil that has hydrangeas in the bed.

Are you adding acid increasing fertilizer for your hydrangeas to the soil? Too much acid is bad for some peonies. Probably you purchased a small root and those do take several years to grow to blooming size. My question was actually is this one plant or several planted in the same area. Which I have seen people do. This fall after it goes dormant brush down through the soil to see how deep they are. Although people keep suggesting raising already established peonies so that they are two inches below the surface I have found that peonies will eventually reach their correct depth. Some are at that depth, some are shallower, some are deeper. It depends on what your particular plant likes. Side note your mulch is too close to the plant it should be around the top not on it unless it is naturally fallen leaves which decay in place.

How much sun are they getting?

Full sun.