Sometimes the sprouts of the main TP's trunk are emerging out of the ground. Those sprouts look similar to the above ground branches.
The sprouts growing from the herbaceous rootstock look differently and should be removed.

Sprout leaves being shaped differently than the TP leaves, is your clue if sprout is herbacous root or a new shoot off the TP itself.

From this group, I learned to plant my TP roots deep, letting the TP grow it's own roots over time and start sending up true shoots to increase the size.

So I usually wait, see what the new shoot looks like as it grows, before removeal or letting it continue to grow. Herbacous Peonies are just a stem, not with side buds for branching out. Leaves are usually coarser, and don't match the TP leaf shapes.

My newest TPs are getting buds, will be their first flowering since planting!! I am excited, they will be like little presents popping open. I think this is the third spring since planting. They were so LITTLE, now ready to flower! They don't seem to be getting up any faster, even with much staring at them, several times a day!!