I have a CB20 save linked to PB21 and I want to transfer my CB20 save to CB21. How would I do it without losing anything?

Well when your CB20 season gets to May 1 (start of a new season) save it and then exit and load up CB21 and use the league import option there on the main menu to bring it into CB21. Then after you have done that, go past the buy reports stage and save in CB21 and go to PB21 and go to Options and change the target of the linked league from your CB20 league to the CB21 league.