As far as I know that combination limits you to a Tesla Model X.seven seater suitable for towing a caravan
EM tweeted that they consider a smaller version at some point but that is likely to be some years away.Tesla Cybertruck will be able to tow 10,000 - 14,000lb. American. That is enough for an American horse trailer with living quarters.
4,500kg - 6,350kg if the UK version gets the same ratings. That puts the Cybertruck in Cat C1 and C1E for towing.
MOTs might be interesting too. MOT Class 4 is for commercials up to 3,000kg Gross. Class 7 is up to 3,500 kg. Over 3,500kg needs an HGV test.
Tow rating may require a tachograph. (There are a few exceptions. EVs are exempt within 50km of home)
Tesla may have to down plate the car so it is legal to drive and tow on B+E. Down plating would also remove the tachograph requirement.