No, you don't have to pay more for multiplayer. There is something weird that happens though if you try to join community content. It will present an error message making it seem like you need to buy something to gain access to the content. It's a misleading error message. So, for example, if you try to join the featured operations by happycamper (or whatever is currently featured), and you get an error message that seems like you need to buy something additional, just go to game settings -> system -> "show player created content": ON. It is disabled by default for some stupid reason. Then close and reopen the game. No more error message. This toggles itself off every now and then on its own, so keep it in mind in the future. And, now you know, closing and reopening the game is required to fix a lot of bugs in this game. Any time you have a challenge that doesn't complete properly, close and reopen the game. Error message? Close and reopen the game. Masterpiece, I know.
Additionally, if you play on xbox (and playstation too?), you HAVE to manually quit the game every time before you reopen it. Xbox dashboard -> highlight game -> hamburger menu -> Quit. Otherwise it never reloads properly. Turn your xbox off without closing the game first? It won't work. Open the game, wait for the error message, quit the game manually, open it again, now it works. Masterpiece.