A French-supported Palestine (as this state will probably be called) is a non starter if the British navy controls the Mediterranean.
It would stupid idea since it would turn his whole Middle eastern campaign into a religious war causing stronger resistance and revolts in Egypt.
No better way to give Selim III's invoction of Jihad in his declaration of war weight...
I don't know...the Palestinians at the time were not exactly known for their love of the High Porte, and that might well change in the event of a protracted war in the region caused not by Nappy's invasion but by the Ottoman counter-invasion (see below for an outline of how to make that perception happen).
The question is: Would the Jews want to go there? Even today, there are some orthodox ones who don't want to go to Israel because their Messiah obviously hasn't come yet.
Were converts considered "fully Jewish" by this point? If so, a fanciful but possibly not totally impossible TL sees Nappy converting to Judaism and being seen at least by some as Messiah.
That's why my suggestion: Get Jews immigrating there. You'll need some hundred thousand at least. - Not saying it'd be a good thing, although things for the Jews in my Chaos TL turned out better than IOTL.
For a possibility on how to do this:
1) Zahir al-Umar's campaigns are much more successful, resulting in a de facto independent Palestine, the Emirate of Jerusalem/Zaydanid Emirate. emerging with Russian support. Rather than/in addition to the Pale of Settlement, Ekaterina II "encourages" her Jewish subjects to emigrate...and if it's educated, well-off Jews who are making the trip primarily, and are submitting to the authority of the Zaydanid Emirate, the Emir and the Arab population won't be making a big fuss. By the time Nappy comes around, the Jewish population is roughly 25% and disproportionately concentrated in the cities. By European standards they might be "backwards" but if they're allowed to actually engage with society and develop I imagine you'll see a vibrant community emerge. And, as all of history up until the 1700s shows, you don't exactly need Enlightenment philosophy to create a functional state.
2) Later on, al-Umar's successor(s) align with the Brits for whatever reason against Nappy, leading to him setting up a Jewish state as an alternative authority in the region, proclaiming the Grand Duchy of Palestine.
It wouldent... if it dident contain large numbers of Muslims who,by definition, must be in a politically and culturally status beneath the Jews for the state to be meaningfully be defined as such. Autonomy for Jews under the Sovereignty of a Muslim state? No problem. Muslims having to submit to a law code based on Jewish customs? No so much.
Presumably, given the time period, the government would be secular at least in name; knowing Nappy, he's likely to appoint one of his family members as duke. They can probably avoid the issue for a while via a continuation of the Ottoman millet system, but yeah, it likely won't be the most stable affair.