proper time to use enhance feature in ACR

I would definitely turn off sharpening before enhancing.

In the screenshot below, the first image has been created from an unsharpened original. The second image has been created from a sharpened original, and shows halos and artifacts from the sharpening.

The first image can be sharpened to look much better than the second, which is difficult to improve.

The third image is a sharpened version of the first, using Topaz Sharpen AI.

I think the Sharpening settings in Camera Raw are not used by the Enhance features (Raw Details and Super Resolution). The interpretation of details in the raw data is what’s enhanced, and then Camera Raw settings like Sharpening are applied on top. However, the existing Sharpening settings are carried forward and applied after Enhance.

So it’s OK if Sharpening was applied before Enhance, but after Enhance is applied you should look at Sharpening to see if those old settings are appropriate for the new level of detail, and adjust as needed.

Below are Adobe articles about these options. These are long articles written by the Camera Raw team, not the Adobe help files that are often less than helpful.

Enhance Details 

From the ACR team: Super Resolution

Detail (Sharpening) is capture sharpening and it done 'visually' so I'd suggest doing so after. 

The steps applying all edits are done at the time of rendering the image, not user applied so you can season to taste at any time, but again, I'd do this after the iteration with Super Resoution is applied but if someone on the Adobe team feels otherwise, I'm all ears. 

I'm not 100% sure, but it looks like the enhance feature ignores sharpening and just works on the base image. So it really doesn't matter if you do that before or after, other than the setting will carry over to your enhanced image, but they can be reset to default.

Willax, which Adobe application or service is your question in relation to?