If you want a clue: Helldivers is not Jimmy's and Hermies work. Is it spelt enough for you?
Helldivers 1 wasn't a live service game, Helldivers 2 is a live service game.
Why would they not be responsible for a Playstation game becoming live service?
You need to decide whether they're responsible for starting a bunch of live service games at Playstation, or that they don't deserve credits for Helldivers 2.
You can't have both.
Also, there were some Playstation live service games out there before Helldivers 2. GT7 and MLB for example.
Jim and Hermen got their current positions in April 2019 (Jim) and November 2019 (Hermen). Meaning, they didn't grenlight GaaS like LBP, PS Home, GT Sport, Dreams, GT7, Firewall Ultra, Helldivers 2, Concord, Horizon Online. All these GaaS existed before them.
TLOU Online and Studio London's new IP pretty likely got greenlighted by Jimbo but not by Hermen.
Jimbo and Hermen did sign Bungie (so Destiny, Marathon, Matter and future ones), Haven (Fairgame$), Deviation's game. And did use their expertise to help the other GaaS teams like Helldivers 2. Plus also obviously helping them with the usual 1st/2nd party mocap, Sony creative arts teams for art, sound, design, localization, pr, marketing etc. teams. Helldivers 2 has been under development for almost 8 years, around half of it under Jim and Hermen, period during which Arrowhead (like the rest of 1st and 2nd party teams) highly grew their manpower thanks to Sony's funds.
The first GaaS MLB was MLB21, so it's possible that it was decided to switch to GaaS during the Jim+Hermen era, but maybe was decided before because it requires a ton of work and yearly releases require a ton of work themselves, so big stuff requires time to be added and isn't implemented from a game to the next one.
Hermen+Jim also grew the teams so people like ND could work -in addition to the GaaS not greenlighted by Hermen- on 2 new SP non-GaaS they have under development and were greenlighted by Hermen and Jim. Same goes with Guerrilla, went from working on HFW only to work on HFW/Horizon 3 (greenlighted by Jim+Hermen)+Horizon Online+Horizon CoM at the same time.
We also know that studios like Guerrilla, Insomniac and Naughty Dog under Hermen's command got rid of crunch, or at least they claim so (or to be working on it, at least to reduce it in the most part).
We also know Jim and Hermen, as did all their predecesors or equivalents in other companies, cancelled games. They cancelled GaaS like TLOU Online, London Studio's game, apparently Deviation's game (if not moved to the new secret SIE team made with ex-Deviation devs) and didn't greelight MP Spider-Man and Twised Metal pitches/prototypes.
We also know that most of the games we know were greenlighted during the Jim+Hermen era aren't GaaS.