You might want to try out Affinity Designer (which is similar to Adobe Illustrator). https://affinity.serif.com/en-us/designer/
With Designer, you can create vector shapes, and apply raster textures or brushes.
"Switch between full featured vector and raster workspaces ... Add raster brush texture to your illustrations, ... mask and add grain to your crisp vectors"
I can't remember for sure (since I have both), but you might need to get Affinity Photo as well as Affinity Designer in order to use the raster features in Designer.
I was very excited when I saw that you can work with vector & raster in the same program. I'm just a beginner with this, but you can check out their website for examples.
At the website above, scroll down to "Vector or raster, you decide" & you can toggle the raster effects on & off to see the difference on a vector illustration.
Here's a short demo video that shows how you can paint raster images, or apply a raster texture to a vector shape in Designer: https://affinity.serif.com/en-us/tutorials/designer/desktop/video/338830412/
Affinity can export as (save as) all the major file types, including .psd — I haven't personally tried sending a .psd file to someone who uses Photoshop, so I can't vouch for it, but I really like the Affinity programs.
