IIRC Sony and Microsoft simply signed a MOU (Memorandum of Understanding), correct? Which is basically them setting some conditions where Sony could potentially leverage Azure in the future if desired, but in the meantime mainly involves the two sharing ideas back and forth?
In other words unless something's changed, I don't think Sony is actually using Azure cloud ATM, but they did upgrade their own existing servers and server software. It's not a 'strategic partnership' the way MS & Sega's agreement is, for instance.
They signed a deal to collaborate on cloud gaming research " to support their respective game and content-streaming services", and said were going to explore -I assume they signed it- to use MS datacenters for PSN (which includes PS Now and more) servers.
Companies to collaborate on new cloud-based solutions for gaming experiences and AI solutions TOKYO and REDMOND, Wash. — May 16, 2019 — Sony Corporation (Sony) and Microsoft Corp. (Microsoft) announced on Thursday that the two companies will partner on new innovations to enhance customer...
news.microsoft.com
So in reality only meant they were going to share cloud gaming R&D, which means allowing MS use Sony's cloud gaming patents for xCloud and share future tweaks they both could make. If the "exploration" was ok (I assume it was the case), then Sony would store at least part of their PSN servers (which includes PS Now and more stuff) on MS operated datacenters.
Datacenters are basically like a big office where you store a ton of server and have an appropiate cooling an security system for them. You can place servers of any kind, an Sony store there their own PS an PS Now servers. Typically companies hire different third party datacenter companies in differnt countries. They are simply a place to store your servers, or optionally hire them. In the case of Sony, they use custom PS3 and PS4 servers for PS Now made by Sony so don't hire them.
Seeing it together sounds like a deal to mostly reduce the price on both sides (one for using patents and the other for renting a place to have their servers), and also share future possible cloud gaming improvements, like the ones Sony later patented related to optimize input lag and improve image quality by using 5G antennas to do some local cache.
Servers are managed remotely, in this case Sony manages the hundreds of PSN servers they have around the world from their own offices, without needing to physically travel there. Sony programs their own stuff they will put in their own servers (like the PSN store, cloud gaming, the games to be downloaded from the store, the PS Blog etc).
But use an app to remotely manage these servers: to upload stuff Sony programmed, to dedicate more HDD or memory to certain server, to restart a server that died etc. There are many differnt apps to remotely manage servers (again, not to program what it's inside them, this doesn't mean that MS programs the PS Blog, the PSN store or PS Now), and the MS one is Azure. These apps optionally offer you to use own their servers, which in some cases is cheaper than to have your own ones. In the case of Sony, PS Now must use Sony made servers using PS3 and PS4 harware, but they could use MS servers for the PS Blog, the PSN store, multiplayer matches or the mobile app since these kind of things run on normal, standard servers.
Regarding the datacenters, this doesn't mean that company -in this case MS- owns all datacenters. Companies like Sony have their own dataservers, then they hire companies like MS who offer them more dataservers, some of which oned by them and other ones instead are "operated" by them (meaning they hire them to a 3rd party datacenter company).