Photos Library did not Migrate over to new Mac.

Did you really use the Migration Assistent and not the Setup Assistent? One problem with the Time Machine backup of your old Mac is, that you need to inherit the backup when you set up your Mac from the backup. You cannot inherit the backup, if you are using Migration Assistant later, at least, I don't know how. When a new Mac is starting up the first time, use the Setup Assistant, as soon as you are prompted to migrate the data. Do not fall for the trap when it suggest you can migrate the data later using Migration Assistant. If you first make a clean install and set up a new user account, you will have lost the opportunity to set up the Mac completely with all user access rights from the old Mac and can no longer inherit the old Time Machine backup for easy browsing. If you use the same drive as before, Time Machine will create a new Time Machine backup, without the history from your old Mac. You may need the "Browse other backups" option to be able to see the files from your old Mac. Hold down the options key while entering Time Machine and select the backup of your old Mac.

If your old mac was dead, where was migration assistant going to get your photos library from?

Where was the library stored on the old mac? In the pictures folder, or somewhere else?

Try holidng down the option key while starting photos. Are any libraries listed, if so select and open them.

So when you look in time machine, and it is not there, how are you looking in time machine?

you need to be entering time machine (use the icon in the menu bar or open the app), then navigate to the date (go back in time to the date you want to restore from) then find the library in the pictures folder.

By default when you first go into time machine it shows the files you have on your mac today - which doesn't include the library since you don't have it.

Have you tried the "option" open of time machine, as suggested by Leonie, to look for your previous backup?