set up file sharing between computers

"Sharing" in this context means, 'make available for others to use.' In the case of File Sharing, you specify the other Users or Groups that can share the files. There is NO reciprocity -- nothing is shared back the other direction.

When you attempt to share, you must provide credentials that would give you access to the original items on the original system. The dialog box is presented on the remote computer screen, but validated on the computer holding the files.

Remember that MacOS is inherently a Multiple User system. If you choose to create only one User Account, that does NOT somehow make that Account the owner of all files. Accounts with the same name on different computers are NOT the same Account -- each computer maintains its own account database.