Herbaceous peonies bloom only once a year, the smallest buds that are not developing are probably sidebuds which bloom after the main flower. Your peony was planted only 1 month ago and did not develop proper roots to sustain blooming, it is stressed out which shows in those brown leaf spots.
It looks your plant is in full sun, so cover it with plastic chair and keep the soil moist but not wet. Overwatering could kill peony by making roots rot.
Do not fertilize it this year.
