Zooming out the problem is micromanaging vs. let those on the shop floor make decisions. You are being told how to work. If everyone but you agrees maybe it is time to consider a move. Your story paints a worldview you have that will be loved by some companies I think.
If it is CTO only and the engineers all disagree. Maybe worth thinking about how to get that voice heard without ruffling feathers.
Try an evaporating cloud! This is a bit heavy to read but is a good technique to think about. It is so good it might change YOUR mind too about this situation! It looks to get to the facts and once practices is a good tool to use.
https://en.m.wikipedia.org/wiki/Evaporating_cloud
Tldr is they want vibe coding because X and you want not vibe coding because of Y. The assumption is Y = !X but if it isn't there could be a good win win.