Official documentation to migrate from Link controller to GTM/DNS

I am not aware of any documentation for that.

Link Controller is a just a limited version of LTM + GTM. In theory, if you change the provision from LC to LTM + GTM, everything should work after.

As you are going to use only GTM after, you need to check what you will lose in relation to LTM.

I would review what services LC is providing, get a lab GTM device, and see if you can configure all type of objects without LTM provisioned.