Nikon picture control to Auto

Lightroom does not normally read/understand Nikon picture controls. (***see note below).

Adobe has created camera profiles that simulate these common ones: Flat, Landscape, Neutral, Standard, Vivid & Monochrome.

Based on your wording I am assuming you are using ether a Nikon Z6/7 camera?

Adobe has not (yet?) created anything that matches this new 'Auto' picture control choice that have been added for Nikon Z6/Z7's or any of the other Creative options like Dream, Sepia, Charcoal etc.

***Note: In the special case of Nikon Z6 & Z7 cameras, Lightroom does read a new section in the Nikon RAW metadata to apply the camera profiles automatically from one of the 'common' ones as above. And it also applies some other basic adjustments and sharpening/noise reduction settings based on info from Nikon in the Z6/Z7 RAW files.

ALL other cameras start off with Adobe Color and use Adobe defaults for Sharpening/noise reduction.

So for your 'Auto' picture control choice it uses the next best option 'Standard', as 'Auto' is unavailable to Lightroom.

You still have the option to change to any of the other available profiles after import or set up as a preset/default upon import.etc.

(you just will not find anything to match 'Auto' picture control')

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I would normally say it is highly unlikely that the profile would be added in the future, but since the Z6/7 represent the 1st cameras that  LR directly uses camera profile info and the other settings then it may be possible if Nikon extends this metadata.

You are confusing an in camera color profile apparently the one named Standard with an Adobe Camera RAW profile, also named standard. They do not relate.

What you want is a camera matching profile.

How to Use Your Camera's Color Profiles in Lightroom

https://creativepro.com/using-lightroom-profiles/

If the profile is set to camera standard in Lr it is using the camera settings as a starting point.

Have you tried a side-by-side comparison using a virtual copy? In this way you can compare the camera profile choices against the Adobe profile choices and go from there.