Well Cortes taking on the Aztecs, which was wayyyyy further away was still done under the auspices of royal authority
Well, it wasn't. Cortes was a rogue capitan, an outlaw for the only real delegate of royal authority, Velázquez (the governor of Hispañola) to send an army after him.
That his expedition was acknwoledged later doesn't make it less of a munity. The fact it happened wayyyyy futher away made it possible in first place : would have he attempted that in Mediterranean...
So again, why not Palastine?
Obviously, Palastine would be doable. But not Palestine.
More seriously, no convenient epidemical shock, no technological advence, no important allies in sight, etc.
All of that would certainly not be a thing.
If we admit we're talking, not of a rogue expedition, but about a real organised and royal-supported one, we still have to wonder why would they attempted such thing in first place.
It was rich and would have made the Pope ecstatic, two things the crown valued.
I think you're giving too much credit to the "Spaniards=Fanatically devoted to pope" cliché. Catholics Kings were about supporting the pope as long he was supporting them.
Undergoing a likely failable expeditions just for him, without real political need to please Rome...
As for the wealth, that's the whole point : Sudanese trade was clearly more promising : wealthier, closer and with less issues about taking over it.
Though I wonder, was the technological difference gap between Cortes and the Aztecs similar to the gap between Spain and the Mamlukes in terms of Naval and Gunpowder?
On matters of naval warfare, Portuguese had the upper hand on Mameluks relatively easily. But, it's likely that the latter would, as IOTL, ask Ottomans for help and Ottoman navy was clearly something else : in Mediterranean Sea, stuck between Mameluks on land and Ottomans by sea.
Let's say it's not going to be a military promenade*
As for the technical difference on matter of gunpowder, the answer is an unquestionable no. The technological difference between Europe and Arabo-Islamic world was virtually inexistant.
You could ask the basileus about Ottoman technological lack in gunpowder...Wait.
*Mother of all euphemism.