So I was having this issue as well and went down a rabbit hole of possible solutions & workarounds (I had already lost an All Companions playthrough at ~40hrs to this bug and was not going to lose another one) and I found one that DID push past this bug, so I registered for the Forums to share my investigation and my findings with you all!
I had the exact same setup as presented here - I knocked her out improperly without knowing in Act I, and in Act II when you meet her again, she was flagged as Friendly (Green), with a speak-to icon on mouseover (the '...' speech bubble) despite not responding when clicked, and neither she nor her guards would leave the area immediately-following the cutscene. She was responsive to spells and abilities used around/on her, and in combat would act as any allied NPC would, yet there was no way to interact with her or force her to progress downstairs, and her quest to recruit her would not trigger.
I decided to reload a save prior to entering Moonrise Towers, and opted to try fast-travelling to an Act I area, and this is where I think I found the conflict.
I had recruited Halsin - if you try to leave Act II after starting the Thaniel questline, Halsin with refuse to come with you; he will stay behind and only reappear in your camp when you return to Act II. I let him go, teleported to the Goblin Camp, and then teleported back to Moonrise Towers to try the cutscene without grabbing Halsin again from camp - and it worked. The cutscene proceeded as-usual, and Minthara and her guards headed downstairs with the quest activating.
Now, I cannot confirm if this is due to travelling to a prior zone 'resetting' the Temporary Hostile NPC tag on Minthara, or if this is some wonkiness with Halsin and Minthara sharing a tent and possibly sharing an internal trigger somewhere that prevents Minthara's quest starting if you have Halsin in-party; I haven't started a new playthrough to try out my theory, nor am I much of a code monkey, but I did, somehow, force my way past this bug. It's not much, but it could lead to a potential temporary workaround until Larian manages to patch this specific issue. I'm not sure how helpful this will ultimately be, but hopefully someone reads this with more technical knowledge than I and can confirm the workaround.
I hope this helps!