User Billy Kerr has already said the essentials and there’s seemingly popped up an answer, too. Here’s a practical way to create the textured colors:
Have a desaturated photo of an everyday material texture. Here’s 3 different.
Insert 2 layers over the texture layer:
A curves or levels adjustment layer to get the wanted contrast; here the contrast is reduced
A layer with the wanted color, the blending mode Color is good for this purpose
Find good combination of the opacity of the color layer and the contrast of the texture layer. All adjustments are non-destructive.
Here’s a screenshot of the curves adjustment. Note: the switch “only the next layer” is ON.
You can flatten the result or export as PNG or use it as is in Photoshop when you make the drawings.
I would draw the images in Illustrator or Inkscape and use exported colored texture images there with clipping masks. An advanced Inkscape or Illustrator user can easily apply layer blending modes also there, it’s not at all a must to make ready to use colored images in Photoshop at first.
As user Daniello wrote, many blending modes work for this. You can colorize a texture or as well you can modulate the brightness of a solid color.
A texture image is imported to Illustrator
A colored rectangle is drawn and lowered under the texture
The rectangles are aligned and the texture image has got blending mode Luminosity, the opacity is reduced – this happens in the Transparency panel.
The rectangles are grouped to keep them together. A random closed shape is drawn on the top
The group and the new shape are selected, a clipping mask is made. For it goto Object > Clipping mask > Make.
The mask shape vanishes. If you need it, for example to get the stroke, have a copy. NOTE: You can allways release the clipping mask if you want to edit it.