How does one transfer old apps from one Mac to a new Mac?
Your best bet for an automatic process is running Migration Assistant on the new / destination Mac. It will ask you to connect the old Mac in target disk mode or connect a Time Machine backup of the old Mac. If you don’t want to use target disk mode - you can also use Disk Utility / Carbon Copy Cloner / Super Duper to make a bootable clone of your old Mac to an external drive and connect that when Migration Assistant asks for the old Mac to be connected.

From there - it can move over user accounts, applications and/or settings and other files from the old Mac to the new Mac.

Lots of good examples here:


Migrating to new iMac, what does Migration Assistant actually migrate?
Recovering all my old settings, apps etc ... from removed hard drive
Best way to move to a new Mac
How can I transfer data from a G5 iMac to an i7 iMac?