“Gonzo” comes from Gonzo Journalism, which refers to a style of writing that is highly subjective and related to the thoughts and feelings of the writer, as opposed to the detached and objective manner that reporters typically strive for. When applied to fiction, it means that those fictional worlds are subjective. In other words, the events that occur in the narrative are done so to elicit response from the characters rather than adhering to a sense of consistent logic or verisimilitude. For example, a monkey wearing sunglasses and riding a skateboard may appear in the narrative to make for an interesting encounter without the need to have some form of “lore” that justifies why this monkey has the ability to ride said skateboard.
Weird fantasy is mostly what you’ve described, just putting twists upon typical fantasy tropes, often giving it a darker tone.
Gonzo has some level of anachronism and a stylistic clash, or a jarring effect. Funhouse dungeons are obvious examples. So are cafes and tea shops serving vegan cuisine, or a high class hairdresser in every farming village. Another big one is inns and taverns. If you're trying to convey a sense of immersion in the setting then the paladin needs to stay with the local knight, the wizard with the local wise woman, the fighters stay in the farmer's hayloft just like the one they used to muck out before they started wandering, and the thief sleeps hidden in a graveyard because nobody wants a thief in their house. But this isn't fun so instead the party stays at Motel VI in separate rooms. I lean toward the simulationist side of things so immersion is big for my games. Maybe you do too.
I mean, there's literally a Conan story with a crashed alien spaceship and a cyborg guy who the people of the Hyborian Age believe is a god ("The Devil In Iron", 1934).
Fafhrd and the Gray Mouser meet a time-traveller from 21st century Germany who flies around in a ship that looks like a big metal snake ("The Swords of Lankhmar", 1968).
Elric time-travels to the 2000s ("The White Wolf's Son", 2005) and the far future ("Elric at the End of Time", 1984), and attends parties in the 1960s with Jerry Cornelius, who is unabashedly a scifi character ("The Final Programme", 1968; "The English Assassin", 1972; "The Condition of Muzak", 1997).
The Dying Earth is a post-apocalyptic scifi setting and a lot of what the wizards do involves pre-apocalypse technology ("The Dying Earth", 1950; "The Eyes of the Overworld", 1966 - the whole series does this but those two deal with it most directly and imo are some of the most enjoyable books in the series).
Zelazny's Jack of Shadows is as powerful as he is because he has a computer ("Jack of Shadows", 1977).
Hawkmoon lives in a far-future post-apocalyptic London and uses laser guns and airplanes ("The History of the Runestaff", 1979).
John Carter goes to Mars ("A Princess of Mars", 1917).
One of Andre Norton's S&S characters (I forget their name) has an adventure in a WW2-era battleship that's randomly thrown into a fantasy world ("Quag Keep", 1978).
Hell, most Sword & Sorcery comes from an era when there wasn't a distinct boundary between Science Fiction and Fantasy. The distinction between the two wasn't even emphasized in publishing until around 1980, and even since, Sword & Sorcery has always blended the two seamlessly.
To me, the hard line that defines gonzo is that there is weirdness and internal inconsistency, but the key is that there is no attempt at reconciliation or reason between the elements.
Let's unpack it!
Gonzo places dinosaurs and secret agents together, and when asked "Why do these exist in the same world," Gonzo responds "Because it's rad, haha, because it's neat!" The second you go "Well because this exists in an alternate timeline where there are three agent factions, one uses the mutogen to create a Dinogenesys Protocol... [insert 600 pages of lore here]" it's no longer gonzo.
Horizon Zero Dawn is absolutely not gonzo, and it's literally about cool stone-age action heroes fighting robot dinosaurs. But then there are literally hundreds of pages of in-game lore that go "actually this is totally plausible"
The least Gonzo setting ever would be like, Tolkein's. He puts dragons alongside Vikings and elephants and angels and stuff. What makes it not Gonzo is his like, thousand pages of unpublished lore development that make Serious Business of the entire project.
Lastly, Gonzo and Weird Horror are sorta like, two sides of the same coin of violating normalcy, one side in order to delight, and one side in order to disturb. "Fungus from the planet Pluto are attacking haha" "Wait what? Where did th-" "There's no time to explain, grab a shotgun!"
If you think that's funny, it's Gonzo. If you don't, it's Lovecraft's "A Whisperer In Darkness."