I don’t think they’re trying to scam you, it just seems like they genuinely don’t know what they’re doing. You need a new mechanic

Checking your owner’s manual will be best, it will probably set you straight.

That said though, take a good look at the spare when you put it on. If it says anything like “for temporary/emergency use only” then you’ll have your answer. It used to be a full-size spare would be identical to the other wheels on your vehicle, and when you got your tires rotated that the spare would get put on and used normally. Full-size spares are so rare these days though that I wouldn’t take it for granted.

Also! Even if it is good to run full distance, it will be difficult to correctly tighten it without a torque wrench. Your owner’s manual will probably mention something about this - it might recommend visiting a shop to get them to tighten the wheel lugs after you mount the spare. I dunno what a shop would charge for that.

You might make your life easier if you talk it out with the shop first. Like mechanic’s liens are a thing, but they can be a slow process.

Also though, never mind what you paid for it. What’s the current value of the Blazer? Is it more than $1400?