I have selected the directory as bitcoin-core directory on start-up.
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what bitcoin-core does when one selects the directory.
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Does Bitcoin Core now ask the user where their bitcoin data directory is when it starts up for the first time? I wasn't aware of this. How long has it done this?
Bitcoin Core should not overwrite a wallet.dat file with a new one if it finds a wallet.dat file in its data directory. You mentioned, when it crashed, you "moved the .bitcoin folder to another drive". Do you still have the wallet.dat file in that folder where you moved it to? If so, then the address should still be recoverable from that file.