Whenever I've tried this, it seems okay if you need an answer to a question, but plain bad if I'm looking for a specific page.
e.g. I'm just now looking for the menu for a local restaurant. "restaurantname menu" in Kagi (Google would presumably be similar) returns a link to the menu as the first result in about a second. Or "restaurantname menu !" goes directly to the menu in about a second.
Meanwhile, searching "restaurantname menu" in chatgpt takes about 5 seconds to return an embedded map from mapbox showing the location of the restaurant. If I click the restaurant pin on the map, there's no menu link, the 667 reviews have no link or way to view, and the restaurant description literally says "I don't have enough information to identify which local business <restaurantname> refers to."
Below the map there's some text: "If you mean <restaurantname> in <place>, here’s the current menu. <restaurantname>". The <restaurantname> link just opens the same card as clicking the pin on the map.
After that there's a bullet point list of the menu that ommits a ton of detail and options.
After that there's finally a link... that I can click to open up a popup at the bottom of the page with an actual link to the menu.
This was literally the first thing that popped into my head, I didn't have to put any effort into finding a query where chatgpt falls on its face.
You might have better luck using google maps (even the web version) to find menus.