This was a 2022 bare root French Prune purchased at Costco (tag states Performance Nursery Inc., Somis CA). I completely ignored where the growth was coming from and now that I am finally able to get to what I call pruning... I find myself at a loss on what to do here. Obviously the root stock is doing great and the French Prune is alive and it does have some new growth. Suggestions?

Do you know if any of those stems are from the original cultivar? If one -is- (like maybe that smaller one that looks different?), now would be the season to cut ALL THE REST off! While it's dormant. Cutting it now won't sap energy from the new season's growth, and all you need do is make sure you don't introduce disease by cutting carelessly. (Most of all: use clean pruners. Very big cuts might benefit from extra protection, but I'm not an expert on this topic.) Best wishes!

@ViburnumValley

Thank you for the reply SkirtGardner. I have prior experience years back of over pruning a tree and it responded with lots of new growth - it kind of went crazy and produced no blossoms until the following year. This seems like kind of an odd case and I am hoping an "expert" will chime in. Thank you.

Do what SkirtGardner said or you won't have any French Prune left. Yes you will get lots of growth and maybe no fruit, but the alternative is rootstock and NO French Prune. There will be lots of sprouts below the graft that you will have to remove or the process will begin again. Remove them as soon as you see them and the Prune will take over again.

It's unanimous. Thank you Skirt & CPP. I will report back in a few months

Just back from a restful vacation; I agree with sentiments and advice provided.

Prune now, or forever hold your (dead) piece of original Prune.

The stem encircled in yellow here is the scion/grafted cultivar, the stem you want to grow and flower (because that's what you bought it for)
The others are stems growing from the rootstock, which is an entirely different variety (most likely an ordinary wild species) that provides disease resistence, vigour or whatever. This is NOT what you want, so these need to be cut off as soon as they appear (it's most likely an annual job too...)