Is it obligatory to stop supplicating for a specific wish and supplicate for goodness in general, or to continue supplicating for that wish, despite the uncertainty of it being good or if Allah has stored something better?

A Muslim should ask Allah to facilitate goodness for him wherever it may be and to make him content with it. If he is compelled to ask for a specific matter, he should condition his request on Allah Almighty's knowledge that it is beneficial and good for him. The former approach is preferable, as scholars have noted. Ibn al-Qayyim says: "Beware, with utmost caution, of asking Him for something specific whose goodness and outcome are hidden from you. If you find no alternative but to ask Him, then condition it on His Almighty knowledge of goodness in it. Precede your request with Istikhara, and let not Istikhara be merely with the tongue without understanding, but rather the Istikhara of one who has no knowledge of his own interests, no power over them, no guidance to their details, and who possesses neither harm nor benefit for himself. Indeed, if left to himself, he would perish utterly, and his affairs would fall apart."