Unfortunately, this is why many people have FLS draw from a bank account that only has those payments in it or don't allow autopay. Sadly they are known for not always drawing the correct amount from accounts.
The correct solution was to return the excess funds to your checking account. If a partial refund was possible they needed to return all of it and initiate a new payment. No part of any solution should end with you being reported late. You made the payment on time and cannot be held accountable for errors that are 100% on their end.
An account specialist can make these adjustments and a copy can be requested to be sent to you in writing.
Instead my understanding is they took the easiest, laziest way out. It sounds reasonable, the forbearance... But FLS had a tendency to leave details out. Like of the excess will go to the principal or the interest? They won't be counted as IDR payments towards forgiveness. And that when they make manual adjustments like this they usually Cascade onto bigger problems. In my case, a manual adjustment almost sent me into default (my payments stopped applying to my account altogether even though they were taking them). What kind of forbearance did they put you on and will interest accrue? If so, at the end will it be capitalized to the principal?
My first step would be getting on the phone to get a copy of everything that they did. Download a PDF of the NSLDS data and of all your bills with your servicer. Make a PDF of any email or message inbox communications. Next you should try to have it resolved by an account specialist. Skip help from the first person that answers your call. Either the account specialist will fix it right then or the logs you've just created (who did you talk to, time, date, summary of conversation, etc) will help you later.
As I described above, you first go to the Ombudsman. Then you go to CFPB. CFPB has no actual authority; they have recently been detoothed. However many servicers are still wary of the threat they pose. They are just a middleman in the complaint because it all helps create a database. It just provides a direct, documented link to your servicer imo prompting a more appropriate response than when you try to call them up.
The other think I want to come back to is that to my knowledge, there is no such thing as payments to ease you into normal payments. If your income is low enough you will just qualify for lower payments. Please check to make sure you're in an IDR (Income-driven repayment) plan of you need the lower payments. If you plug your income into the repayment estimator while you're signed in it should easily tell you what your payments will be in each plan.
Good luck.