Sony pays the server costs of the cloud gaming, online chats in parties, trophies, matchmaking, friends management, shareplay, online leaderboards, cloud savedata, remote play, PSN store, microtransactions/dlc, plus some of the player stats/metrics etc. for both 1st and 3rd party games both SP or MP, paid or free.
Other than that, some games use dedicated game servers for the in-game multiplayer gameplay itself plus (including SP games too) game specific metrics/player stats. Publishers can decide if they provide their own dedicated servers or if they use (paying a portion of their cost) PSN ones.
Part of that PS+ Essential tier also goes to pay the monthly games plus discounts. There's also some profit that (like the one from games and addons) that goes to compensate to sell hardware at a loss, something that happens in a big scale unlike in the case of Steam or Epic Store.
We have the numbers:
The graph of the left explains why GaaS are important for the future, because add-ons (DLC/IAP/passes) keep growing every year, already are a huge part of the game revenue and are projected to continue growing in the future.
The graph in the right shows that they weren't almost investing in GaaS and will invest a lot there, but also plan to invest more in non-GaaS than before (notice the dark blue part will be taller in FY25 than it was in FY19 and FY22, even if the percentage is smaller.
To make GaaS like Destiny 2 or Gran Turismo 7 is more expensive than a non-GaaS AAA because to develop all that post launch content and pay the servers isn't free.
They already have in the market Destiny, Helldivers, MLB, GT, Firewall.
Have in the works Concord, Marathon, Fairgame$, Convallaria (not sure if GaaS), Bungie's incubated project moved to PS Studios.
Cancelled TLOU Online, London new IP, Deviation (maybe not completely but being rebooted in the ex-Deviations new SIE studio).
There are more that now I forget, in development or cancelled but may not be part of these 12 IPs with GaaS initiative.
In 2021 they originally said that had March 2026 as deadline for the 12 IPs with GaaS initiative, but later as they kept reviewing the projects mentioned that some of them may not be on time, so dropped the deadline in order to give them whatever time they needed because they wanted to prioritize quality over quantity.
Jim Ryan also mentioned that they didn't expect them to have a big success with all of them, and that they were going to have different scales (example: I assume they hadn't huge expectations for a VR only GaaS, or for the Helldivers sequel).
It's also fair to assume that after this big push pretty likely they'll tone down the releases of GaaS titles and will focus their GaaS investment during several years on post launch content of those who performed better.