Did legends Arceus run on the same servers as the other 3 mainline switch games?

I know with scarlet/violet the servers are different as gen 9 allows trading with mobile hotspot. I ask this because sword and shield hate mobile hotspot and don't allow trades from hotspot. I guess the main 3 I'm concerned about are bdsp, la, and legends 2. Will legends 2 run on similar servers to sword and shield's or scarlet and Violet's? Does legends 1 and bdsp accept trading via mobile hotspot or do they "spit it out" like sword and shield? Not concerned about lgp/lge as these are possibly easier to obtain using the trade corner for version exclusives.
 
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