They're all right, just different perspectives and markets.
The private collector is likely very knowledgeable and has bought them for this or less but hasn't fully factored in how much the gold price has gone up, nor has he seen how much it's pulled prices up.
The dealer I'd be a bit wary of, the send it to me for inspection then $2,500 is often send it to me then find 20 reasons to offer you less, but at that point he has the watch, you've already paid for shipping, and you're likely to agree to a lower price to get the deal completed.
Then coming from the opposite direction, you have chatgpt which is assessing the price based on the asking price of every hopeful seller or dealer on the internet. It's looking at Chrono24 asking prices, eBay buy it now asking prices, not actual selling prices, so it's telling you what some people who have one to let go hope to get.
Real transaction prices are sold listings, no reserve auction results, etc and many dealers will make an effort to hide the reality that a watch listed at $6,000 might have actually sold in the low 5K range.
Reddit is mostly people bouncing in between the Chrono24 asking price, for an example that's been gathering dust in a shop window for 4 years, and some actual recent transactions for the same, or a similar watch.
If you own a London vintage watch shop and Barry, who's dad once owned a Conquest and always wanted one like it in gold comes along, it's an $8,000 watch, but the odds of Barry ever darkening that doorway are extremely low.
If you want to sell it, you list it in a no reserve auction on eBay and you will get the market price, it's literally a feeding frenzy of dealers and collectors pouring over every listing, it's an extremely efficient market, and that will be the current price it is worth.
