Really curious to see how this one plays out. As you say, past halvings say it should go up, a lot. The more institutional nature of many BTC holders should make it less volatile, which may also mean the increase, if any, will be moderated. And the increased demand with even more restricted supply says it should go up.

Perhaps, it will drop post-halving, but much less than the last three times, then it will climb, but more slowly than before, and then it will continue going mostly up as demand vs. supply requires.

Only the future will tell.