If you have other bank accounts at the same bank then yes those banks can see your other bank accounts on their computer system.
However if your other bank accounts are at different banks then no the banks cannot see other bank accounts of yours at other banks that are not owned or operated by them.
Now if you have more than 1 bank account with the same bank branch and you visit another branch of that same bank then yes the other bank can look up your bank account information and can give you cash from another branch of the bank or allow you to deposit money into your bank account at another bank as long as it's with the same bank and branch of that bank.
But if the banks are not the same banks and not owned or connected with each other then no those banks cannot see other bank accounts at different banks.