I’ll suggest that your question on proton beam therapy should be more refined. I and some others who write here have received proton beam therapy (PBT) as the first level of treatment for Prostate Cancer (PCa). That said, I think your question might be more targeted as “Does Mayo Clinic use PBT for treatment of PCa outside the prostate?” Of course any kind of treatment depends very much on the particulars of your specific situation.

On a quick google search related to PBT and metastatic PCa I did not find a clear answer on Mayo’s website. I did find a clearer statement on Johns Hopkins Hospital website. See: https://clinicalconnection.hopkinsmedicine.org/news/proton-therapy-faqs-for-prostate-cancer#:~:text=It%20is%20a%20curative%20alternative,the%20adjuvant%20or%20salvage%20setting.
It does specifically mention the use of PBT pencil beam scanning as the technology used for PBT delivery. I’m about 99% sure that pencil beam scanning is how my PBT treatment was delivered at Mayo Rochester.

Some in your post prostatectomy situation are referred for ‘salvage radiation’. That may be an attempt to radiate a broader area without specific targets. ~such as if the assumption that PCa cells are likely present but in a quantity (or mass?) below the level that would show on a PSMA PET scan. I believe that metastases that are clear on a PSMA PET scan could be treated with PBT. The advantage of PBT is the ability to ‘target’ a specific site and minimize irradiating not involved tissues and organs.

Best option would be to move forward would be to submit all your records to the Mayo site you prefer (Rochester is bigger, so more docs/appointments). Their style is to have an initial appointment and then add other appointments as dictated by your circumstances and mutually agreed upon treatment.
You might ask (anywhere) what the lag time is between agreement to get PBT and getting on the schedule. With my treatment for PCa their was a needed time to program the equipment. You may also need to have fiducial markers inserted that provide a point to guarantee positioning for multiple PBT treatments . With primary PCa treatment I believe those are inserted into the prostate so not sure of the need in your situation.

I’ll assume that your doctors are also suggesting a course of Androgen Deprivation Therapy (ADT) aka chemical castration. You might search Mayo Connect for others experiences on ADT. There are also some suggestions for a regimen to counter negative side effects of ADT at the prostate cancer research institute http://www.pcri.org