People pray for the sick to be healed, but they’ll never pray that an amputee will get their limb back, so isn’t that a sign they know there is no real god to answer their prayers?
Really neat question. People use the term miracle loosely to refer to any answer to prayer, narrow escape from danger, etc. But these things are not literal miracles. Allah has ordered the creation to behave according to certain patterns which we study and attempt to describe by way of science. A miracle can be of two types, either of which involves a clear, pronounced deviation from those patterns. One type of miracle is a mu’jizah, which serves as a sign of a person’s prophethood, like when Allah made the moon split at the order of Prophet Muhammad, peace on him. The other type of miracle is a karama, which is like when Allah allowed Umar, Allah be pleased with him, to see and talk to someone many miles away without a device. When people pray it is not that they should expect these types of miracles, but that they know Allah knew their request before they even made it and that they know Allah has power over all of creation.
The prayer of someone in thirst is not to ask Allah to miraculously place a glass of water nearby or to suddenly fill the stomach, though Allah can do that, but, rather, to pray for drink and then to go seek it. Furthermore, Allah may answer in ways that are not expected. In the case of an amputated arm, an advanced prosthetic might be an answer to prayer. Or peace to find the purpose of losses can be an answer to prayer. The Prophet, peace be upon him, said, “How amazing is the affair of the believer. There is good for him in everything and that is for no one but the believer. If good times come his way, he expresses gratitude to Allah and that is good for him, and if hardship comes his way, he endures it patiently and that is better for him” (Muslim). The believer understands that this life is short—difficulty and death are certainties—yet everything is an opportunity and we do not know Allah’s plan. In this way prayer is only partly focused on present circumstances but more so on navigation to success in the hereafter. Nevertheless, if someone were to pray to Allah to replace an arm or leg, even while Allah is capable, the answer may come by way of protection from some other calamity or by way of vast reward on the Last Day, which will be a more lasting answer.
Supplicating to Allah is real and has real results as part of a relationship and life journey, perhaps in ways that would not be readily understood without embarking on that journey. Allah often answers quickly and clearly. Yet Allah is not a jinni in a bottle or a servant for us to order. Allah is the Lord of the Worlds, All Wise, Who says, “Perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you.” Prayer comes along with trust and patience as Allah knows that of which we are unaware. It also comes with the realization that even while we may want to control everything, we have very limited wisdom and foresight. And so it is from Allah's Mercy when Allah holds an answer to prayer until the hereafter rather than granting it us in a time that may not be good for us if we only knew.