I struggle to understand how orbital data centers can make sense. Is it mainly for continuous solar energy? Surely this can't be enough to offset the costs of launching?

See the recent Dwarkesh interview with Elon: https://www.youtube.com/watch?v=BYXbuik3dgA

Continuous 5x solar power (relative to on earth), no earthbound construction red tape or protestors, and yeah it can only possibly pencil out with Starship launching routinely. No other rocket system could even come close to making it work.