When migrating printers (including printer shares, drivers, ports, queues, and printer settings) from one server to another, its pretty straight forward.
Ensure on the source server the Print Management Server role is installed. If not, install it now.
On the destination server, install the Print Management Server role.
On the source server, launch Print Management
Right-click on the Print Management and select Migrate Printers from the context menu

Choose to Export printer queues & printer drivers to a file

Follow the process to the end of the export
On the destination server, launch Printer Management
Right-click on Printer Management in the menu and select Migrate printers
Select to import printer queues and driver files from a file

Locate the source files

Choose whether to keep existing printers

After this is completed, the new server will have all the same printers, queues, drivers, ports, etc as the source server. You can now go through the process to update the various printer deployment scripts or GPOs.