It was uncertain whether running normally or running whilst crouching was faster. So I decided to test it. Most characters seem to go at the same speed or just a little slower whilst crouching.

Soji and Shigeru go at a much slower speed while crouching. Of course crouching once before you start running is useful as you get full momentum/running speed instantly.

I found it's also useful to do before reaching/opening a door after running for a while. As this stops you from bonking/slamming into the door.

Here's the comparison: