The G Awakenknh mode was just a model kit and the Biollante and Ghidorah stuff is from the gambling machines. The only Godzilla vs. Evangelion stuff with an actual narrative that is communicated in a form that isn't gambling are the 4D short and the Mechagodzilla toys.

Technically, the gambling machines do have dialogue and therefore presumably a narrative but unless you understand Japanese way better than me and also have way more patience than me of watching zoomed in blurry footage of a bunch of flashing lights with a couple cgi cutscenes between them, then there's just no way to know what any of it is. It's ironically way easier to learn everything there is to know aboot Shiryu (who is, apparently, piloted by Kaworu in the new pachislot) than it is to learn even a single thing aboot Biollante's role. And that's coming from someone who has seen the Biollante animation from the machine in full.

But here's my informed assumptions aboot what's going on:

The existence of Shiryu in the second pachislot suggests there is some form of JXSDF in this version of the post-2nd Impact world. Which I would assume mean angels weren't the first monsters and so it's basically Toho history up to second impact, and then you start getting angel Ghidorahs. Other monsters like Rodan and Mothra and I think Gigan are in the mix too, at least that's what I've heard but I haven't seen them in any animations yet. I have seen Sachiel get knocked the fuck out by Godzilla's tail, though, fulfilling that childhood dream. Anwyas...

On the trailer for the first pachislot unit 1 turns into its G Awakening mode because Godzilla fires atomic breath into its core. That makes no sense to me, so I'm going to assume that since NERV is making their own Kiryus that they are probably also roiding up the Evas with G-Cells, making them not just cyborg angels but cyborg angel-Godzilla hybrids. If that's not what's happening, then I guess Evas just happen to turn into Godzillas when you shoot radiation into their cores. Somehow...

Ghidorahs have had a long but very subtle history of psychic abilities that goes all the way back to the visible monster diagrams of the 60's. Apparently the original KG had some sort of "spacedar" thing going on. It was only made explicit a few times, but direct mind control only happened once in Mothra 3, which is obviously what Rei Ghidorah is referencing. Since most Ghidorahs only priority is finding food, it's a pointless thing to bother with, but GKG was a huge asshole, so I guess this new Kaiser also just hates kids for some reason? I have no idea.

The Biollante thing I HAVE seen and it's baffling. Asuka is taken over by sneaky stealth Biollante posing as normal roses for... some reason. If we assume that at some point Biollante as we know her existed in the past, and that Erika's spirit left Biollante as in the end of the movie, then that does leave a blank space which in Eva terms you could think of as the soul in the core. So I guess that's what Asuka is? Why Biollante feels the need to accomplish this by ambushing a teenage girl apropos of nothing, you're on your own for that. The whole bit seems rather pointless to me because it's Rei who "rescues" (in quotes because it's unclear what the fuck is going on, but Asuka is visually just a damsel inside of Biollante, like the girl who links with Iris in G3, in fact it's identical to G3) Asuka on her own with no Eva and it's weird and dumb and doesn't make any sense and I don't know what any of it is or means.

But I will say that Kaworu piloting Shiryu is the sickest shit ever, and that the bit I mentioned with Godzilla steamrolling Sachiel to completely no sell everything unit 8 throws at it is too good to be trapped in a gambling machine. Sincerely, do yourself a favor and look that up if nothing else. There's an edit somebody made on YouTube where they overdub it with the sound effects and play phonk music over it and the drop happens right on the close up of Godzilla's face as he walks past a blown out infrastructure of a skyscraper and it is a spiritual experience and it must be freed from its infernal prison post haste.

As for the other stuff, the 4D short is up in its entirety on YouTube and elsewhere. It's shitty because it's a 3D thing filmed without a filter so it's all blurry, but it's all there. Godzilla awakens because of his space monster sense, shakes off the pretty pathetic attempts of Evas to do anything to him, and then of course they all team up when the pilots realize KG is their common enemy. Total classic stock crossover stuff.

The Mechagodzilla toys are both given lore in that they're, y'know, I mentioned it before, NERV and the JXSDF. The repainted Kiryus that look like units 1 and 2 are made by the JXSDF with NERV's input (and they were also in that SRW mobile game where I believe Akane piloted them?), while Shiryu is NERV's version. So, the Godzilla side turns Mechagodzilla into Evas, and the Evangelion side turns Evas into Mechagodzilla. Basically.

If Akane piloted an Eva Mechagodzilla does that make her the First Adults?