The first things to check are, maybe,
- You are looking at the wrong Photos Library
- Your Library isn't the System Library
- Your Library isn't connected to iCloud
So
#1: with Photos closed, option-click the Photos icon to bring up the Library Chooser. It might look something like this:

As you see, I have several Photos Libraries. If you have more than one library, you can load and check those.
#2: the Favorites Library is my System Library. The System Library is the Library that apps, like Messages, or Screensaver, or Safari, go to when they use a picture or save a picture in Photos. It is the only Library on a Mac that can synchronize with iCloud Photos. The Library Chooser shows which Library is the System Library. If you want to change that, then go to Photos' Settings>General

Here, "Use as Photos System Library" is grayed out, because it already is.
#3 If the Library you're using is the System Library, you can check to see if it's connected to iCloud at Photos' Settings >iCloud

If you have room on your new iMac's drive, the best setting is Download Originals so your pictures can be backed up.
Let us know what you find…