They don't
need to register a UK company at all to do any of this, but it neatly keeps all uk activity together for them as non-residents.
As for using the SOL, it is meaningless. They could buy the club with a company registered in John o' Groats and it would make not a blind bit of difference, but a more practical idea for people who only have a collective interest in the UK is to register it at the SOL, have all of the companies house and other paperwork sent to SAFC and forwarded on as necessary.
I don't see it as a big statement of intent, neither that nor the due diligence would be unusual for the type of deal they did, given where they come from and how little pre-existing infrastructure was in place to keep everything together for 3 separate people involved in a project here. Everything about it screams temporary vehicle for convenience (including shutting it down), and if anyone thinks they were somehow convinced to do a deal they didn't want to do because they didn't' agree with Donald's valuation, they are on another planet or they're not the owners we want