2001 Mustang GT grinding noise from front drive side

The wheel bearing would do it all the time no matter what, and I doubt it's bad. They can take a beating. My guess by your description would be to check brakes/rotors etc. The "low pad indicator" might be hitting the rotor and when you apply the brakes there's usually enough pressure to make it go away a bit, but it will come back once released as you say. Check those items first. The noise should be there always no matter what gear if it's brakes. Just have to go slow enough to hear them.

Sometimes a bad wheel bearing will also make a different (or change) in the noise when making slow speed turns in one direction and not the other.

My experience with wheel bearings is that they make noise when the hub is spun with no wheel or rotor in place. In my experience the noise sticks out like a sore thumb.

I would also suggest check the caliper slid pins to verify they move freely. If the slid pins are galled to the bracket this could cause a greater side loading and thus making the noise change.

The front hubs on my 2000 GT lasted over 200K miles before they started making noise. Only one did make noise. However I replaced both due to the car's high mileage.

I had the same issue when I bought my car it ended up being the wheel well had came loose behind the wheel and was rubbing I put a new body pin in and haven't had any problems with that since how ever I would definitely check the brakes mine looked fine from the outside looking in but the inside was wearing way more and was catching just not making any noise