Bags will be checked all the way through, no need to pick them up. No need to pay again for bags.
Note that at SFO you will need to transfer terminals. Thus will include needing to exit the secure area, get over to other terminal, and reclear security. This is because of setup of gates, nothing to do with how it was booked. Not sure about SAN.
I would contact DL. Something else surely has availability then connecting on three non-partner (AS and UA arent even partners) airlines with two connections.