I bought and downloaded 1 and 2 on the PS5 in preparation to binge it all in 3.
Not OPs fault but the info there made me more confused instead of less lol. What do I need to buy or download or do to get everything?
Go into 1 and redeem the Legacy Pack DLC for 2. Since you bought 2 digitally, that should actually be all you need to do. I would say to keep both installed for the next few days just in case there's anything weird, but you should be fine.
Also... if you haven't already started anything, don't play 1 by itself. If you want to play anything in advance, just play 1's levels inside 2. There is no way to transfer progress out of 1, while 2's progress will be able to be transferred to 3.