This is my first barrel swap on a savage (or any gun)

Presently I have a brand new 270 that I put 3 rounds through and removed the barrel and have a shilen 35 whelen barrel to install.

I have a go gauge ( no go is in the mail & a notched barrel nut)

With the a shilen barrel screwed in and headspaced on the go gauge the barrel has a little bit of movement.... is this normal ? if I screw the barrel all the way in then there is no movement

So is barrel movement normal with a barrel screwed into the action without barrel nut?

Or should I be concerned with the action and or barrel threads