I have a tool for creating Tailwind color palettes you might find interesting here (https://inclusivecolors.com) where you can visualize how the hue of Tailwind's "gray" shifts a little to the left and the saturation goes from high to low as the gray gets lighter (you'll need to load the palette first via "Import" then "Tailwind"), and customise it if you want.
Their "neutral" is the perfect gray you're looking for.
Why their "gray" is actually blue, I have no idea.