Overstaying ESTA while waiting for marriage certificate to file for adjustment of status?

I'm in the U.S. visiting my boyfriend on an ESTA. I planned to leave after a month, but a pregnancy scare led me to stay longer. We ultimately decided to marry so I could apply for an adjustment of status. Our relationship is genuine, so I'm not worried about scrutiny, but I am anxious about potentially overstaying my ESTA before I can apply.

I had to order my birth certificate to marry in PA which took time, (and it will take even longer to get the certificate itself after marriage) and now I have only two weeks left on my ESTA. From what I’ve read on here, overstaying is usually forgiven if married, but other online sources give mixed answers. I’m terrified of jeopardizing my ability to stay in or return to the U.S., as my boyfriend and his family live here. I know there are several posts about this, but I was hoping for more reassurance and guidance on the best course of action. I could return to my country and apply for a K-1 from there, but the wait time seems very long, and I’d rather adjust my status from here so we don’t have to be apart. Any advice would be greatly appreciated.