I can't imagine Disc World as a functional RPG setting, but then again Toon was a thing.
But then again, I never played Toon.
But then again, if you are going to go this route, it seems to me that Toon is perfectly functional here. Certainly, "If it is funny, then it happens", should be a rule.
The underlying problem with such games is that they only work with a player group composed entirely of stand up comedians. Humor isn't an ingredient that just magically appears out of a rule set. You can't say, "And it was funny" and it be funny. At least, not more than once.
Discworld is presented differently in different parts of the series.
On some occasions it's presented as a serious world but where madly comedic things happen to the protagonists, but in the background it's pretty much a standard fantasy world (especially prevalent early on, when Ankh-Morpork is almost completely a reskin of Lankhmar).
In some books, the world is absurd but the protagonist is the Only Sane Person around and is having to deal with the world being insane whilst they're relatively sensible.
In others (particularly the Sam Vimes and Granny Weatherwax books), the protagonist has a great understanding of the world and has to use that knowledge to overcome problems, with varying degrees of comedy.
But quite a few times, the world is kind of dark and threatening, and Pratchett doesn't pull his punches on treating the world as a more threatening place. There's still comedy, but its a bit bitterer and angrier. Arguably his very best books -
Small Gods, Night Watch,
Monstrous Regiment, and
Nation for his non-
Discworld books - fit into that category.
So there's plenty of different approaches you can take. I'm actually regretful that Ed Greenwood and Terry Pratchett didn't follow up on an idea they once mooted of doing a comedy
D&D adventure with the Ankh-Morpork City Watch (or light reskins thereof) getting jobs in the "proper serious fantasy city" of Waterdeep and seeing how they'd fare, possibly as a charity project.
Pratchett's biography is also worth reading for the sections when he was running D&D games after work in the local pub whilst working at a nuclear power station. Some proper bonkers stuff, including Pratchett roping in passing drunk visitors to play NPCs and getting so annoyed by players losing track of their arrows and treasure that he spontaneously created a magical TARDIS chest running around on little feet to carry all their gear.