the parents can research what the service does in detail if they wish.
If you are claiming that COPPA allows "implied consent", you are flat out wrong. Parental consent must be explicit.
Every school consent form I've seen in the past few years includes 'may lead to the disclosure of personal information' someplace in the body text.
If their disclosure says that, they should be fine.
What level of consent is needed in your view?
My view is utterly irrelevant. All that matters is the view of the judge your lawyer is trying to convince that your organization was COPPA compliant after a parent sues you.
Look, this is not complicated. Google for "COPPA checklist", click on the first link, then read it. If you are compliant, fine. If not, fix the issues to get in compliance. That is all.