I transferred from iPhone 12 to iPhone 13. Apps started loading but stopped halfway. It says loading under each app. Has been this way 24 hours

You need to connect to a stable wi-fi network and connect the iPhone to power to keep the wi-fi active. Do this until all of the apps have finished loading. If connecting does not get them started again, power the iPhone off and back on gain while connected to power and wi-fi and that should get them started again.

if the problem is that the apps won't finish loading it is not helpful to say connect to the power until they do. clearly the answer should be 'power off' then reboot- ie restart the new iphone and connect to wi-fi. But does loading of old iphone apps then restart automatically, os is there a button to press? problem is that the apps say 'loading' or 'waiting' for days without doing anything!

While powering off or rebooting the phone may be necessary, it not always is. If that is what it took for you, then fine. The loading of the apps should start automatically, especially if you had to reboot. You also have the option to tap on an individual app and you should see an option to resume download. Each individual can be different, depending on what point things were at when you disconnected from wi-fi.

with sim in iphone? in the new iphone 13 or in the old iphone?

Which iphone should be connected to the laptop/wifi?

Make sure your iCloud Keychain is on.