Lost Photos

Did you make sure, that the photos have already been downloaded from iCloud Photos to your Mac?

Check the troubleshooting, mentioned in this article:

Get help with iCloud Photos - Apple Support

Set up and use iCloud Photos - Apple Support

Are the photos greyed out in Photos for Mac?

As your computer is new, I assume the system version given below your question is no longer valid? A new computer should come with macOS 12 Monterey.

As a test:

• Open your iCloud web page at www.icloud.com.
• Sign in with the AppleID you have used on the old computer for iCloud Photos.
• Click the Photos app at www.icloud.com.

Are your Photos there and can you select and download them?

If your photos are still in iCloud, connect your Mac to Wi-fi. A cellular Hotspot may not suffice to download the photos. Also disable temporarily any Firewall or Anti Virus software that might be interfering.

Enable iCloud Photo on your new Mac:

• In System Preferences > AppleID sign in with the AppleID you used previously for iCloud. Enable the checkmark for iCloud Photos.
• Launch Photos and go to Photos > Preferences.
  • In the General tab click "Use as System Photos Library.
  • In the iCloud Tab enable iCloud Photos.

Then wait for the Photos to download back to your Mac.

If you should get any warnings preventing you from turning on iCloud Photos again, check the free storage in iCloud and on your Mac.

• It is not possible to enable iCloud Photos, if your Photos Library does not fit into iCloud in addition to the photos that are already in iCloud. In that case move your current Photos library to an external drive to save it. Then launch Photos again by holding down the options key and selecting to create a new, empty library. Now make the new library your iCloud Photos Library. Photos should now allow you to enable iCloud Photos.
• It will not be possible to enable "Download Originals" if the photos from iCloud will not fit on your Mac. In that case use "Optimize Mac Storage".