Can the Quranic verse, "He said, 'Your prayer has been answered,'" be considered an indication of a supplication being answered after prayer and a request for a sign?

What happened to you is an act of optimism, and it cannot be definitively stated that it is a sign of a prayer being answered. The answering of prayers is not limited to the fulfillment of what was requested. Allah may answer a prayer in one of three ways: He may grant the supplicant what he asked for, or He may avert from him a harm similar to what he asked for, or He may store up the reward for him in the Hereafter. We advise you to recite the Quran frequently and ponder its meaning, for there is immense reward in it.