Trying to Move my Photo library to new Mac Mini

Where are you planning to keep your Photos Library on your new Mac? And are you using several Photos Libraries and want to switch between them? There are two things to consider:

1. The System Photos Library: You can have several Photos Libraries, but only one library can be your System Photos Library. Only the System Photos Library can be seen in the Media Browser in other applications, for example in a web browser or Mail. The System Photos Library needs to be on the internal volume or on an external drive that is always connected, when you are signed into your user account, or Photos may lose the connection to the library and create a new, empty library in your Pictures folder. If you do not have enough storage on the internal disk, keep the external drive with the System Photos Library always connected, while you are logged in, even if you are currently not working with the library. The background processes need the access to the library.
2. The file system format of your external drive and the file ownership: Any external drive you are using to store a Photos Library needs to be prepared as described here, or the library may become damaged: Move your Photos library to save space on your Mac - Apple Support Make sure, the external drive you are using to move your Photos Library between your Macs has a compatible file system format (MacOS Extended (Journaled) or APFS), and the "Ignore Ownership on this volume" flag set, even if you are just using it to copy the library between your Macs. Otherwise there may be problems with conflicting pathnames or the file ownership.

To make the copied library your System Photos Library double click it to open it in Photos and open the Photos > Settings > General: Click on "Use as System Photos Library".

Copy the Photos Library from the Pictures Folder on the old machine to the Pictures Folder on the new machine. That's all you have to do.