ETA: I have now discussed this a little bit with moderator Jerseygirl. She suggested 2 possibilities:
1. Maybe your vet didnt do a full castration, I e a full oviario-hysterectomy. A spay is technically just a hysterectomy. It is not as common these days as it used to be, because it means the animal will still produce sex hormones and display all hormonally linked behaviors, such as false pregnancies and territorial marking. The animal cant get pregnant though and it can get uterine cancer because there is no uterus.
2. When a bun is de-sexed at a very young age, the ovaries are tiny and can sometimes not be found during surgery.
It does seem over the top with 3 false pregnancies post spay and also this very vigorous urine spraying. That a bun sometimes pees when it’s being pet and is all relaxed and comfy is not too uncommon though, my bridge bunny Bam did that even though he had been neutered for years. Preferably in my mom’s lap because that was his favorite place.