I chose BM Classic Gray for my bathroom. To me it's more neutral than gray, not a cool gray at all. This doesn't answer your question, but might be something your interested in.

This will make you groan because it's often viewed as a tedious step, but the best advice is to put swatches of each color on the walls and look at them at different times of the day under different light conditions.

You'd be amazed how different a shade will read depending on whether a room gets southern or northern exposure to natural light.

There really is no substitution for testing the colors in your space and different light through the day. For a suppposedly neutral color, greys can be tricky. Fact of the matetr is that a greyy can be any color plus black or some canceling tones.

Revere Pewter goes violet on me and Edgecomb grey a bit green in some rooms. I wound up going to Sherwin Williams and trying their colors. Agreeable Grey was the right tone for my living areas, but I am doing them at 150% to get a little deeper color. I am using Anew Grey in my entry and stairwell -- that hasn't been done yet. .

More important to your question about going with cool and warm colors -- the Agreeable Grey in my FR had to work with red brick, cherry hutch and dark wood floors as well as blue, green and white in the upoho;stery, rug and kitchen cabinets and counters. Anything that tended green made the red brick fireplace more intense and anything too warm made it pinker/orangier. Agreeable Grey at 100% was too light -- was too close to my grout and looked chalky, so we just added more color and went to 150%. SInce it is a light color to begin with, it is still light, just richer. The result was amazing -- my red brick calmed down. No more orangey, purpley/brown red. And it is so soft and neutral with the blues,, green and white. We did the ceiling at a reduced value. It was the first time I had used SW paints and as much as I liked BM, I was just as pleased with this job (DIY).

Take a look at SW Repose Gray. Very neutral, looks great in rooms with or without natural light.

BM Grey Owl is a very neutral grey, IMO. (But I love SW Agreeable Grey)

Grey is SO on the way out.

I like gray, but would consider it for only one room, not a whole houseful of it. You really have to do what you love in terms of color and what works with your furniture and accessories. Gray has been around for so long now that it may well be going out of style. When beige was "in" I never had a single room in that color because it was often done so badly and I really didn't like it. Not every gray room is successful either. It has to go with everything in the room.

Look at Sherwin williams agreeable grey. It's a warm grey, beige, very similar to edgecomb grey but slightly less green. It will look different in every room because it changes with the light.

Don't be fooled by the name "gray" or "grey" in a paint color. Some really aren't gray at all.