UPDATE: I've found the wallet.aes.json file of the wallet and was able to decrypt it with the same password that the site claims is the wrong one.
What should I do next? Should I "import" it (using this link -
https://login.blockchain.com/wallet/import-wallet)? It is already in their system, so maybe "importing" isn't the right thing to do.
Importing it to that link will create a new wallet with different Wallet ID and other credentials, but the keys from your imported wallet.aes.json will be added there in a separate wallet.
Better use it only if you have no other options.
Can I use this file to gain access to my wallet from another site, or is this file unique to blockchain.com?
Yes, you can decrypt the file to get an unencrypted 'wallet.json' file to view the contents in readable format.
Like in this reddit post about using OpenSSL:
restoring_blockchaininfo_walletaesjson_fileOthers may have a better solution.