How do I replicate this misty spray paint texture/pattern?
If the material is metal, one can use a wrinkle finish powdercoat to accomplish this result. It's not quite exactly the same texture, but wrinkle finish powdercoat may qualify in that it's random and irregular.

Using search terms "texture powder coat" provides a number of similar finishes, including hammertone and silver vein, the latter shown below:



If there is a powder coating service in your area, they can advise of the available finishes. You can also purchase a home powder coating system which can be used with an inexpensive (yard sale) toaster oven for small parts.