Well, assuming that, I’d expect them to be liable for repairs to restore the car to its prior state (most likely replacement with a used engine).
Now that I’ve answered your question, I’ll tell you that I think you asked the wrong question, and that your assumption illustrates the old saying that when you ASSUME, you make an ASS out of U and ME. What you describe does not indicate a seized engine.
It’s virtually unheard of for an engine to seize without making some significant noise first. You mention no noise.
A starter trying to crank a seized engine makes a single resounding thunk, because the engine cannot rotate at all. It would not sound like anything grinding, or anything moving in any way at all for more than the initial split-second thunk.
There are dozens of possible causes for an engine to die while driving. Are you only thinking of a seized engine because you feel you can blame it on the last people who worked on the car? I find it strange that you talk a lot about oil/lack of oil/oil leakage/etc., but do not state that the oil level in the engine was actually low. Did you even check it? If not, I respectfully suggest that you’ve met the ASS qualification in the saying I mentioned. If you did check it, I’m wondering why you didn’t say so, seeing as it would be a MAJOR piece of information leading to question you posed.