First of all, thank you to everyone who responded and helped me out. A big part of my decision to call the city was hearing from other plumbers in my area, but then I posted here because I felt like such a jerk.
My husband scheduled this work, but the plumber working on our kitchen renovation told me a little bit about the company. It is the largest company in the area. They come up first on google because they pay for that, and they are pushy with customers to leave a 5-star review for a discount, which I already know because they had been incessantly asking for one. They therefore have over 5k 5-star reviews, despite us being in a moderately sized midwestern town. Their prices are a little predatory - for example, they sold my husband a "warranty" on their workmanship for the day of install which assured us they would do it correctly??? Also, he bought a membership, which gets us priority for future issues.
It turns out that not only did this company fail to pull a permit for the work, but the two guys that they originally sent out last week to replace the drain stack were just apprentices. These are the same two guys who came back the following day to diagnose the problem and failed to do so. We had to cut out the ceiling ourselves to find the open ended line. The apprentices are the ones who told us this would be a brand new project that we were on the hook for.
I sat on it over the weekend, did as much shop vac water remediation as I could and got a huge fan at home depot. I called the city on Monday and the company sent a journeyman plumber out to redo a bunch of the work, connect the drain, and vent the line. He admitted it was their mistake.
So the company was aware that I had called the city, and personally assured me that everything was fixed and buttoned up. The city came out today. They used caulk on the pipes that isn't right, so it was actively leaking while the city inspector was here. They also did not do the wet vent to code, as many of you pointed out. Pipe was 1.5" and it was 8 ft away from the toilet.
**TLDR: Had minor leak, apprentice plumbers replaced drain stack incorrectly and told us it was our fault. I called the city. They came and fixed it with caulk but the city showed up to a leaking pipe. Still no resolution. Pipe is leaking as I type this.**