Dentist Billed Me 3x The Written Estimate After Treatment, Am I Actually On The Hook For This?

Location: Minnesota, USA. About six weeks ago I went to a new dentist for a cracked molar. Before anything was done the office manager printed me a treatment plan with a total of $1,450 for a crown including the prep, temp and final, and I even asked "so this is the total, nothing else?" and she said yes unless something unexpected comes up. I took a photo of the estimate on my phone because I'm the kind of person who does that. I did NOT sign anything other than the general consent form and a HIPAA thing at the front desk.

Fast forward to last week, I got a bill for $4,380. The itemized statement shows a "core buildup", "periodontal scaling", "surgical crown lengthening" and a bunch of other stuff that was never discussed with me at all. The dentist did mention during the appointment that he "cleaned up a few things" while I was numb but I assumed that was just part of the crown prep. Nobody told me there was an extra cost or asked me to approve anything. When I called the office the manager (a different person than the one who gave me the estimate) said the estimate was "just a ballpark" and that the final cost depends on what the doctor finds. That's not what I was told and the printout doesnt say ballpark anywhere, it says "Estimated Patient Total" and thats it.

They told me the account will go to collections in 30 days if I dont pay in full. I already paid my insurance portion and my copay, so the $4,380 is what they say is left. I'm willing to pay the original $1,450 but not triple that for work I never agreed to. Do I have any legal leverage here, is a written estimate binding in any way? Can they actually send me to collections while I'm disputing it, and would that hurt my credit? Should I send a dispute letter first, contact the state dental board, or just pay and move on? Honestly kind of stressed about this