In my opinion it’s obvious gen 4’s lore is connected to gen 7’s, just as it’s connected to gen 2’s.
I can begin to understand why you would say Gen VII is connected to Gen IV, but Gen II? What? Why?
Ultra Beasts are Pokémon from other dimensions that look very peculiar. Well guess what, this definition applies to Arceus, Dialga, Palkia and Giratina too, all of which have their own dimensions.
Even if we ignore the rampant speculative nature of that remark, there's still a problem with that suggestion. Ultra Beast isn't just a mythological concept, it's also a modern-day scientific classification. If Arceus and the Sinnoh Trio fit into the classification of an Ultra Beasts, they would be acknowledged as such, at least ambiguously like Lunala, Solgaleo, and Necrozma. There's also the fact that even if we want to assume they all originate from the their dimensions, they're all separate dimensions entirely. And if they're separate to each other, than there's no way they can all come from Ultra Space. Ultra Beasts are not Pokemon from other dimensions, they're Pokemon that come from Ultra Space specifically.
If anything, it’s just a matter of Sinnoh not really having come in contact with ultra wormholes like Alola and therefore they don’t call them the same way. It doesn’t make sense to make a distinction between them with the info we have. At least not yet.
Your logic is completely backwards here. The fact that we have nothing connecting the two but pure speculation means we should be making a distinction until actual evidence is given. I'm sorry, but everything you're saying is nothing but your personal head-canon. It is nothing but pure speculation on your part with no facts to back it up. There's nothing wrong with having a head-canon, but you shouldn't try passing it off as fact, especially as an obvious fact.
There’s also the fact they created type: null from knowledge about Arceus specifically to make a ‘Beast Killer’ implying it’s kinda seen as the only thing that normally would be able to control them perhaps.
Or maybe they just wanted their living weapon to be based off of the most powerful Pokemon to ever live. That would make for a pretty good Beast Killer regardless of Arceus' relation to the Ultra Beasts.
Also remakes don’t have to happen in the same gen to be relevant. Game Freak loves creating a massive interconnected lore and limiting it to games of the same gen would go against this vision, same reason why I don’t think we’re done with Mega Evolution yet too
That really isn't true. The only cross-generational stories we've ever gotten outside of remakes is Looker and parallel universes. Beyond that, we have nothing but a loose assortment of cameos and easter eggs.
I'm honestly expecting them to clear up the differences between all these dimensions, because it's getting a little silly lol. One of these professors studying UltraSpace should hopefully know about Sinnoh Lore too, and thus they should, even if quickly and vaguely, explain how UltraSpace differs from other dimensions.
What really needs to be cleared up though? We have an assortment of different dimensions, each with their own inhabitants. What more needs to be explained? There doesn't necessarily need to be anything that makes Ultra Space any different from the other dimensions, all that matters is it is a separate dimension.
Although I do expect them to also be connected, as we see in the dimensional lab that they have files on Girantina, Palkia, and Bronzong, so there has to be something similar!
It also mentions other non-Sinnoh Pokemon with dimensional-related abilities, as well as the Inter-Dream Zone from the Dream Radar game from Gen V. The fact that you see mostly Sinnoh Pokemon mentioned is purely because Sinnoh had the most dimensional-related Pokemon due to its nature.
Also, this is random, but in looking around at information about the Dimensional Research Lab just now, I found out that Professor Burnett is the same character from Dream Radar. Never knew that before. Extremely strange.