I removed the 980 Pro and put the 4TB SN850X into the console. Then, I bought an M.2 SSD enclosure for my 980 Pro. In doing research, I learned a lot of M.2 SSD enclosures are NOT compatible with PS5. I did find one that is compatible, however: The ASUS ROG STRIX Arion enclosure. It came with a USB A 3.1 to USB C cable that you can plug into the back of the PS5, then plug into the enclosure. The cable, however, was defective. I had to buy another cable from Anker which worked. There's also no heatsink necessary as the enclosure acts as its own heatsink.
As for the transferring, unfortunately, if you transfer games from the internal drive to the 4TB SSD, you can't just insert it into the console. If you intend to keep the 4TB SSD as an external drive, then do what I mentioned above and get that enclosure. But if you want it internally in the console, then you'll have to download everything all over again. It's a pain, but with the amount of space you'll be left with, you won't have to do that again for a long time.
Also remember, you can't play PS5 games off of the external drive, only PS4 games. Even if its an M.2 that's compatible with the console. I tried. You can store PS5 games there though. This is why I switched out the 980 Pro for the SN850X. What type of heatsink are you using with the 980 Pro?