That is very strange, never have I seen a picture of a OEM Bergara with a barrel nut.
Is this a newly manufactured Bergara or an older one?
When Savage introduced their barrel nut many folks thought the nut thing was rather ugly. In around 15 years ago Bergara was selling their Remington barrels with a smooth nut and they marketed it as being prettier than the Savage nut and that required a strap wrench (as seen in the video posted above). If I'm not mistaken that was before the Remage craze. I have a 26" SS 6 grove Bergara with this nut I purchased about 12 years ago.
I'm not familiar with the Bergara bolt, on the Remington I strip the firing pin out of the bolt which isn't necessary but the bolt is smoother to work. If the bolt extracts the gauge it has most likely been seated into the bolt face past the extractor, otherwise the gauge will remain in the chamber.
As @INTJ has stated about insuring the chamber is clean, that also applies to the gauges and the bolt face.
I torque the nut between 50-60 ft pounds, and then again check the headspace. Depending on the tools being used sometimes the headspace will move and it needs to be set again. It is a small learning curve.