I have direct experience.
I have traditional/original Medicare (not Advantage!) with a Medigap policy.
I have lung cancer and pulmonary fibrosis.
My pulmonologist tested me and then wrote my oxygen prescription for 2L continuous flow for EXERTION and SLEEP. My O2 is normal when sitting.
The prescription went to an oxygen provider (who accepts Medicare and bills Medicare directly), and they delivered to me 1) a stable oxygen concentrator (for night) 2) an Inogen One G5 portable with bag, charger and ONE standard battery.
After two years I noticed Sieves needed changing so I called my oxygen provider. They came out and brought an Inogen Rov 6 and took the other POC away.
So if you have a valid prescription for portable O2 and you work with a provider who accepts Medicare, then you are only dependent on WHAT THE PROVIDER WILL HAVE IN STOCK AND GIVE YOU. At least that was my case.
I also have them come out twice a year to check my stable concentrator to be sure it is working properly.
Another issue is how long do those batteries last!!! Portables like Inogen are pulse rate not continuous flow. I have to set mine at 4-6 when I go out. Medicare only gives you one battery so to travel, also have backup, one has to buy at least one more battery and the standard is about $400
P.S.
You mention Main Medical Rochester. Mayo sent me home with Oxygen from Lincare after my surgeries, so I used them for portable also. They have offices in many places in the US