from Lightroom to Photoshop/camera raw update problem

An annoyng problem, for sure!

I suggest it might need a full clean of all Adobe 'stuff' from your computer and re-install LrC and Ps (with ACR) all totally afresh.

Have your LrC catalog backed up then use the Adobe Creative Cloud Cleaner tool.

Creative Cloud Cleaner

Only one other thought check your computer for instaled applications to see if you have more than one version of Photoshop installed. See the screen capture from my Mac.

Ok it may be possible that you have more than one version of LrC installed on your computer.

With the version of Lightroom that you are using and is presently opened select the option "About Lightroom Classic" and see what is displayed on the popup dialog.

Yes, it is 9.3

As said by DdeGannes it is not Camera RAW but your version of LrC. You are more than likely still at 9.2.1 and not 9.3.

Not sure what you can do about that as the CC DTA states you are up to date. BUT you might have 2versions of LrC installed and you are opening the older version.

The Adobe Creative Cloud app is showing that the Camera Raw Plugin in Photoshop is 12.3.

You need to ensure that you have LrC v9.3 installed and being used to send the file via Edit in function.

In PS, check your plugin info, looking to see what v of ACR it is using.

https://helpx.adobe.com/photoshop/kb/uptodate.html

>It's frustrating because after I edit the picture on Ps and send it back to Lr, my original color profile is gone, making the photo impossible to edit.

You should realise that when you edity a picture in Photoshop all the original Lightroom edits get rendered into a tiff file and you will not be able to go back on any of the edits you did before you sent it to Photoshop. This is inherent to the way Lightroom and camera raw work completely differently from Photoshop and cannot be prevented. You can in principle open the file in Photoshop as a smart object and then you can go back to your camera raw settings inside photoshop by clicking on the smart object but that limits what you can do in Photoshop.

Is there any chance that you have two versions of Camera Raw on your computer? That can confuse things.