It's a common UI/web design trick now to brand your color palette more by mixing in a little of your primary color into your "gray" swatch. Gray gets used a lot so this has a subtle but noticeable difference. Tailwind has a few gray swatches you can pick from (https://tailwindcss.com/docs/customizing-colors) where "neutral" is all gray if that's what matches your brand.
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.
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.