In a real fight, the F-35 smokes the F-16 beyond visual range before the F-16 even knows there is a problem. The radar and electronic warfare capabilities are incredible.

Isn't modern tactics to not use onboard radar but to be driven in by airborne radar from AWACs? Or is it used once in the furball as the jig is up at that point?

Modern tactics are to use every radar around via datalink (AWACS, Ground Station, stealthy drones flying ahead). The onboard radar is last resort, but still very capable.

Right, so I wonder what difficulties they are having with the F-16 to retrofit the new package to receive the same datalink.

The US is stuck with older F-16s than the current export models with advanced radar. They're gradually being upgraded with some Block 70 components. That requires the new cockpit so it isn't just a quick part substitution.