You should have used setup assistant/migration assistant to set up the new Mac.
Things would have gone easier that way.
But...
The transfer can still be done.
PRINT OUT this reply and follow it step-by-step as you work.
First:
You want to use a PHYSICAL DRIVE to do this job.
It can be a hard drive, an SSD, or even a USB flashdrive of sufficient size.
It will serve as "the intermediary" between the two Macs.
Next:
Connect the drive to the OLD Mac.
Navigate to home/pictures
Copy the "Photos Library" icon to the drive.
(note: the Photos Library is not "a file" ... rather, it's a folder with A LOT of other folders inside)
Then:
Disconnect the external drive, and take it to the NEW Mac.
Now:
Connect the drive to the NEW Mac
Let the icon mount on the desktop, but DO NOT OPEN THE DRIVE ICON YET.
Click ONE TIME on the drive icon to select it.
Now, bring up the "get info" box (you can type "command-i")
At the bottom of get info, click the lock icon and enter the password you are using on your NEW Mac
Put a checkmark into "ignore ownership on this volume".
Close get info
Next step:
Before going further, I'm going to ASSUME that your new M3 doesn't really have anything in its existing Photos library.
Is this correct?
OK, then do this:
On the NEW Mac, open your home/pictures folder.
DELETE the existing Photos library and empty the trash. We don't need it any more.
Now:
Drag the Photos library on the external drive into your home/pictures folder.
Does it copy now?
If so, we're almost done.
Open the applications folder so you can see all the apps in the finder
Hold down the "option" key and double-click Photos.
You should be asked WHICH LIBRARY to use?
OK, you should see the Photos library (which is actually from the old Mac).
THAT'S what you want to use, so click it and continue.
Does this work for you?
This sounds like more work than it is.
The important step is to overcome permissions problems by choosing the "ignore ownership on this volume" which we did above...