iCloud Photos does not sync to Photo Library located in my External Drive

When I called Apple Support, they told me that it was not possible to have the Photo Library in an external drive connected to iCloud. So they took me through to the process of backing up the Photo Library as a file in iCloud Drive (which is different from iCloud Photo). But since the file was so huge, the process could not get through. So, there was no solution for my request.

So I decided to try another way. 1) I exported all the pictures from the Photo Library to a new folder in the External Drive. 2) I created a new Photo Library in the local Mac, 3) I made this new Photo Library the System Photo Library, and 4) I moved it to the External Drive. 5) I deleted the newly created photo Library in the Mac and later 5) I assigned the Photo Library in the External Drive as the System Photo Library and deleted the Photo Library in the local Mac 6) I connected the Photo Library in the External Drive to iCloud. It worked. So, this Photo Library, we could say, is a fresh file with no strings attached and no bugs. 7) Finally, all the pictures I exported initially were imported to the System Photo Library.

As an additional step I created an Alias in the ....user/pictures/ directory heading towards the System Photo Library located in the External Drive.

Hi, yes, otherwise it does not allow you to select iCloud. I checked both, the System Photos Library and then the iCloud Photos as shown in the images!