Even though the doctor generally has a higher "status" than a patient, it can definitely happen that a professional doesn't know what to do and how to deal with both being professional and having feelings (positive/negative) that get in the way.

If I were you, I'd be happy to have had the courage to bring it up, the rest is just your doctor showing that she is also a flawed human being. Nothing bad, just uncomfortable.

I hope you don't beat yourself up over it and face the future with just another bit of experience under your belt.

He should have not kept things like this from you; regardless of whether or not he feared consequences or did not find it relevant.

Don't focus on what happened, focus on where to go from here. Let him know that you want to respect his decisions, but that you also want him to give you confidence that your future together will not be tainted by this issue.

His commitment to holding his word is commendable, but it gives you stress so see if there is a way that reduces it: perhaps you can set up an automatic payment that ends at a given date, perhaps he'll just donate the remainder of the money in one go, or perhaps he'll quit altogether if no solution can be found...

Either way it's not unreasonable for you to ask him to communicate to his ex that outside of the money he will cut ties altogether (if he really does despise her, but she still has an influence that might be the better solution for him as well. If it is, he will know it too)

I hope for you that a reasonable solution can be found for all of you.

His finances are ultimately his, but he should care about your feelings too.

Either find a way where he continues to support while giving you enough confidence it will be confined (either in it remaining platonic, not increasing in size or quitting altogether).

He wants to help her, but he should also realise that such support should have its limits. Perhaps he hasn't thought about or maybe he already has decided. Talk through it together and stick to the outcome.