Is Musk still planning to do his art-project lunar flyby with Starship? Haven't heard anything about that for... is it years now?
For the catching mechanism they're going to want a second tower, for which the parts are only just starting to arrive at Starbase, so it'll probably be at least 6 months until that's assembled, and closer to 12 until it's through simpler testing and ready to take on a real catch. So probably a good 4-5 years until they're ready to put any humans onboard, and then another year or two after that to put complete amateurs onboard.