You may not have prepared the old Mac so it is current and also may not have migrated properly when you copied so please read on!
Current versions of Mac OS no longer no longer support 32 bit apps. Apple advised you for many years however you have misunderstood or ignored the messages. On your old Mac please update your legacy apps to their 64bit counter part versions. If you find any that cannot be upgraded (the developers of the apps need to do that) then replace them or decide if you really need them. You can use System Information to look at your legacy third party apps to determine which are 32 bit or you can use the Roaring Apps tool to find what you have that is 32 bit.
After upgrading all the legacy apps on the old Mac that you want to keep then it is time to migrate. How you do that is first backup the old Mac using Time Machine. Once you have it backed up then simply execute the steps in Setup Assistant and Migration Assistant and you are done. If you have already started adding stuff to the new Mac then you may want to start over by doing an Erase and install so your migration starts with a clean slate.