As you have spotted Stellantis have suspended the former Fiat Storico certification service, but this has no impact on UK registered cars as DVLA often refused to accept the Fiat certificates anyway.
I'm the DVLA Liaison for LMC and am not aware of any changes beyond the new and actually less rigorous rules for modified cars over 40 years old.
Once your car is registered as 'Historic' no further action is required as far as I'm aware? LMC can provide the necessary certificates to obtain Historic registration if the vehicle was registered some time after manufacture, otherwise you just apply with you V5 the April after the 40th anniversary of registration.
Perhaps you could post a link to the video?