AUTO and PROFILES are greyed out

Normally, when you open a photo in Develop, LR initially greys out Auto and starts calculating in background whether the current develop settings match those that would be applied by Auto. If they're different, then it enables Auto and ungreys it. This typically takes no more than a second or two after opening the photo in Develop, even on older computers.  

But in your case, not only is Auto greyed out, but the Profile Browser is also greyed out:

Someone else recently reported the same symptoms:

https://community.adobe.com/t5/lightroom-classic-discussions/auto-and-profiles-are-greyed-out/m-p/14966182 

They discovered that you could also enable the Auto and the Profile Browser buttons by zooming to 100% and then back to Fit.

In years past, there have been problems with the asynchronous display of other settings in Develop that are worked around by zooming to 100%, e.g.

https://community.adobe.com/t5/lightroom-classic-bugs/p-quot-built-in-lens-profile-applied-quot-isn-t-always-displayed-for-embedded-lens-profiles/idi-p/14032567 

Zooming to 100% loads up the Camera Raw cache with the photo as part of rendering it, accelerating the Auto and Lens Profile computations.

I believe, based on years of observation and forum posts, that internally, the implementation of Develop is fragile, with many "race conditions" where the correctness of asynchronous computations is timing-dependent.  Such race conditions typically show up only when some part of LR is abnormally delayed, e.g. because LR is running with a slow or absent GPU. or trying to display a very large raw.

A couple of things you might try to ameliorate the problem:

1. Build 1:1 (100%) previews either on Import or with Library > Previews > Build 1:1 Previews.

2. Do Preferences > Performance > Camera Raw Settings > Purge Cache. Perhaps the current cache contents are causing it to perform extra slowly.

3. Restart your computer. If the problem persists, try resetting LR's preferences as suggested above by AxelMatt:
https://www.lightroomqueen.com/articles-page/how-do-i-reset-lightrooms-preferences/

LR sometimes soils its preferences file, and resetting it can fix all sorts of wonky behavior. That article explains how to restore the old preferences if resetting doesn't help.

4. And if none of this helps, then as suggested by AxelMatt, do the LR menu command Help > System Info and copy/paste the entire contents here so we can see exactly which versions of hardware and software LR thinks you're running and important LR options that are set.

Happy it works for you too. I suspect this has something to do with the "Adaptive Profile" that is present in ACR but not in LrC. Apparently the picture needs something done to it for the Auto/Profiles to be activated now. From where I sit, that looks like a bug to be fixed soon enough...