Transmediterranea sail from Barcelona to Palma; at this time of year there's a choice of day and night sailings, taking about 7.5hr.
https://www.trasmediterranea.es/en/
London to Barcelona can be done in a day; leave st pancras at 09h22 and arrive Barcelona 20h34. since the ferry port is only 15mn by taxi from the station, you can catch the night ferry and be in palma less than 24hr after leaving London.
there's no night trains from paris to Barcelona, the excellent trenhotel ended when the high speed line to Barcelona ended. but you can still take a night train from paris to port-bou (on the border) leaving paris at 21h00 Fridays/Saturdays and arriving at around 10am. the run from there to Barcelona along the coast is a nice ride.
for working out a leisurely point-to-point itinerary the best journey planner is that of the german railway -
https://reiseauskunft.bahn.de/bin/query.exe/en?