In my case it ended well but it that was by chance.
So I bought (yet) another PS3 (I intend to gift this one to a friend). I know I (or they) would want to mod it eventually, and if I'm buying a PS3 with that in mind, it would probably be a good idea to get a model that supports full CFW.
I found a posting on FB Marketplace of a PS3 slim, and the seller took photos of the console from all directions, including the bottom, and they were very high-res, allowing me to discern not just the model number (CECH-2504A) but the date code as well (1A). Other than 21xx (which for some reason I find difficult to come by recently), the 25xx is probably the best model to mod, with the only asterisk that it must have been manufactured before April 2011 to support CFW. Date code 1A means Jan-Mar 2011 so they are all CFW compatible.
Anyway, when I actually got the console, the date code was actually 0C. Turns out the seller had a stock of PS3s he was selling, and while he did know that people might be interested in the model number (which is why he took a photo of the bottom), he was not very knowledgeable about modding and did not know that the date code matters for 25xx, so he created a single listing for all of the 25xx consoles he had.
In my case it wasn't bad - 0C consoles are also all CFW compatible and can actually be downgraded further than 1A (all the way back to 3.40; the 1A are either 3.50 or 3.56), but it could've also been a non-compatible 1B - again, the seller was not aware of the difference.
And this was a seller that at least knew that the model mattered - other people on FB Marketplace or eBay might not know that it does. They just know that it's a fat / slim / super-slim. You might see a photo of a reliable CECHK and get an unreliable CECHH, or see a photo of a CFW compatible 21xx but get an incompatible 30xx.
Lesson of the story - If the listing does not explicitly mention the model and date code, don't trust the photo, don't be lazy. Contact the seller and verify exactly what you're getting.
Cheers.