They had a joke of a case. When they first threatened to sue after I'd given notice, the CEO told me he'd have to take legal action to set an example for the new company. Or as the head of HR put it "they can't take our best people." They made no mention of trade secrets or any other legitimate business interest that would have been required to enforce the agreement in court. Instead, the CEO said that they had a "basically an open and shut case" because I couldn't take my "work experience" to their "closest competitor," which is nonsense. Not to mention that people at both companies have told me the companies weren't even competitors.
But the new company withdrew the offer to avoid having to go to court, so the facts and the law didn't matter.
This is how non-competes work.
The legal threats almost scared me into staying, but then I thought about how miserable I would be if I went back there. The postponement of the promotion had been the least of my complaints, nothing else would be getting better, and I'd only be inviting further bullying in the future.
So I left. I didn't get sued because the new company dropped the offer before I started. I was unemployed for a couple of months and also spent a significant sum on a lawyer. The whole thing was expensive and stressful bordering on traumatic. But I've never regretted turning down the counteroffer.
My current company tried to get me to sign a non compete by leaving it on my desk. I dropped it in a drawer and now everyone's forgot about it. No one is ever going to remember to get me to sign it. The main thing that weirded me out about this one is it also said I can't recommend that any of my current coworkers come work with me for something like 2 years after I leave the company.