Local Drupal installation can't copy files to another computer on network
Go to the MAMP console under "General" tab, go to the setting for "Run Apache/MySQL server as user".

It should be setting to www (Apache) / mysql (MySQL).
So you need to change it to username (Apache) / username (MySQL).

Save and restart the servers

Refresh the browser, then change it back to www (Apache) / mysql (MySQL), save and restart, and everything should be working