I wish I knew why the writers think that they need every crossover to have its own timeline/universe.
It's likely because Urobuchi doesn't want to interrupt his narrative for crossover material. To make the crossover actually fit in the running plotline, they'd obviously need Urobuchi's participation too, considering how Gaim has a serial storyline. It doesn't seem like he wants to play with them though. To be fair, considering how this is Takebe, I wouldn't be surprised if they were mostly last minute things, rather than events planned from the start.
The crossovers kind of get acknowledged, but it's always in things not connected to the script, but mainly direction. For example, the Beat Rider teams and the bgm for the final Beat Rider episode all matched Sengoku Battle's Beat Riders, but that's mostly casting, props and direction, the script itself has never acknowledged Sengoku Battle's events.
Toqger Vs Gaim shows the repaired Yggdrazil Tower (with the destroyed domes back in place but not spinning anymore), before the actual Gaim series itself showed it, but the tv episode continued right after the last one without a break.
This episode apparently had a disclaimer about taking place a while ago, but obviously nothing from it has been referenced anywhere either. We likely will see the new Invess type introduced here appearing in group scenes of minor Invess though (and it's included in the list of Invess in the official website), but the script won't mention any of the events we saw here.