Sims show 5, but I would say that number comes with caveats. Here is an example game.
https://pastebin.com/9ceEzqmp
In this game player 1 is guaranteed to win. Because both players are "perfect," player 2 also knows this, and kinda "gives up." Or in other words, plays randomly. But the move on turn 4 is obviously a bad move for p2, because it's a guaranteed loss in one.
So, if you mean in all cases, then yes, 5 is going to be the least turns until game ends (I couldn't construct a game that purposefully loses faster than that), but that may require a player to lose faster than what may be "normal".
Changing the heuristic so that the bot extends the game as long as it can (more opportunities for a human opponent to make a mistake) is on my to-do list, but will be a slightly more involved change, so I'm putting it off.
Fun fact: Collapsi has 378,378,000 unique states. (16!/(4!4!4!2!2!)) This isn't counting the fact that if you shift the board left or right, the board is technically the same due to wrapping. (I think that's /12, so 31,531,500 but not confident.)