You have too many teams, so to prevent your browser from freezing and crashing when you open the backup/restore all page, it gives you your teams in a compressed format known as packed format. You can import a packed team into showdown just like an unpacked one, you can also restore all your teams from that large list of packed ones.When I try to backup my teams it comes up as a large block of text instead of something I can paste into a pokepaste. Is there an easy way to solve this?
As for saving it to pokepaste, why can't you just save it there? Its just text like anything else. The only thing is you wont be able to scroll through and view the details on the pokemon easily. If you actually can't consider an alternative storage medium like emailing yourself, pastebin, or saving it to a text file on your computer.