Nah I just have a background in the trades and understand sometimes people get an estimate and think it’s a binding contract.

Yes the shop should have called OP. OP doesn’t have to pay the increased costs, but that doesn’t mean the way they went about negotiating was good behavior. This isn’t a situation where only one party could be the asshole. The shop didn’t post here asking if it was an asshole so I didn’t offer a perspective there. OP went with manipulative tactics when they could have simply brought up that they didn’t approve an increase in labor. There were much better ways to handle this and still only pay what was quoted.