I'm not a mechanic either & there's not much information to go on here but if a pulley is smoking, is something locked up? Like if it's the AC compressor & that locked up, you might notice the lil centerpiece that the belt wraps around won't be spinning like it's supposed to. If it's an AC compressor though I can't imagine it would cost you a thousand bucks 😶 that'd be expensive AF in my opinion. But then again I don't go to shops so I might be biased. I replaced an AC compressor last year for $150 but obviously I didn't charge myself labor... Shops like to charge you for everything they could think of.
Like I said though, I'm no mechanic, I just wish I could help people out in situations like that because I know it's a pain in the ass & I hate seeing people pay so much for little things. I'm hoping you have a good reliable shop 🙏 let us know how it goes