As the title says, I'm looking for spells/effects that will cause creatures to move, like one of the effects from the Confusion spell. This is different than "forced movement" like a push/pull/teleport, in that the creature is using its own movement.
Ideally I could combo this with Booming Blade, so while the Command spell qualifies as making the target move, it won't do so if the command is "directly harmful to it". But whether or not it works with Booming Blade (or Opportunity Attacks), I'm still looking for these kinds of effects.
Best Answer
Two spells I have used to trigger opportunity attacks
fear
dissonant whispers
My warlock or bard, respectively, often casts one of those when one of my party members is in melee and if I am successful (the enemy fails the save DC) then my allies get an opportunity attack.
I have seen command used to this effect as you mention when another caster used that in a similar situation. (Confusion should also work, but I haven't seen it at the table). You could expect that the antipathy/sympathy spell to have similar effects.
From the 2019 Sage Advice Compendium (page 8)
Clerics and Paladins: turning enemies
Turn undead uses the foe's movement if they are undead; and against fiends, celestials, fey and elementals if the cleric is of the Arcana domain.
The Ancient Paladin's Turn the Faithless does something similar to fey and fiends.
Caveats: I don't self proc the effect, as you suggest. Depending on the version of booming blade that you are using (SCAG or Tasha's) there may be an issue with using the warcaster feat's feature to self proc the Opportunity Attack. When they changed the range to (self) it appears that the OA option using booming blade was curtailed, whereas the SCAG version was for normal melee range and worked with booming blade.
What is willing?
That's somewhat answered here, and it appears to have no consensus and attracts hair splitting. Discuss it with your DM/your table and come to a consensus that you all can agree upon.