"It says that stretching / range of motion exercises are very helpful to heal neck strains, and not harmful at all."

Stretching and strengthening a strained neck - in my experiences - can both help and/or hurt depending on the stretch and exercise. I saw lots of chiropractors, a PT, and did other work before I learned I had to listen to my body and neck.

It's not a black and white answer. It depends.

Being immobile can be very bad. I did that and my muscles atrophied and my neck got stiff and lost its range of motion. Being to aggressive with the activities can be bad too. I say listen to your body. Go slow. Symptoms can flare, so be aware. The neck affects the brain a lot and vis versa.

The challenge is listening to your body and doing what it needs. Find the sweet spot where you get enough movement with your neck but not too much.

Lastly, seek help if you need it from a professional.