Modern Vespa

2004 ET4 4k miles surges when idling. This had sat for a long time. Work done relating to spark, fuel, air:

New plug
New cap
Tank drained of varnish smelling gas
New fuel tap
Fresh gas
New carb
New fuel and vacuum lines
New throttle body
New air filter

Idle screw set at 2 1/2 turns out

Video link to hear surge

Any ideas?

https://drive.google.com/file/d/1LadFOCmrstDWYEtjHC68rseST6frPw0o/view?usp=drivesdk

The idle mixture or air/fuel screw is not set correctly, so you're idling off the throttle slide. If you cannot get it to idle by setting the air/fuel screw correctly, there's likely a carburetor in your future.

This is a new carb that was was bought from you. Is it defective?

There is no special number of turns you turn the screw in or out, or there wouldn't be an air fuel mixture screw. You need to warm up the bike, and then set the air/fuel mixture and throttle screws, based on how the engine runs, not any fixed set of turns. Also, even though it's new, make sure the pilot jet is clean. Sometimes they suck up crud that was in the bottom of the tank, and it doesn't take a lot to clog them.
When you say you replaced the throttle body, what are you referring to? And is there anything in the gas tank that's not gas?

Here is what I called throttle body

Intake Manifold p/n 849465

In listening to it, it definitely sounds like it's idling off the pilot jet circuit, and not the idle circuit. if you turn the air fuel screw in all the way, does it kill the engine? And it looks like all the evap system is still intact. Since it's been sitting for a long time, you might find a split in one or more of those hoses, or dry rot.

Thank you. I will look into that

Removed evap stuff. Sounds much better

https://drive.google.com/file/d/1wGYvbo62d-qpyAIwC-ipIzJ9eBuDUwid/view?usp=drivesdk

It does sound a lot smoother. You could likely fine tune the air/fuel circuit a little, especially if it's a hard to start. That's another symptom that it's idling off the throttle and not the idle circuit. But if it's firing right up, and not surging at idle, it should be good to go.