On the technical side, I added a bit of a canvas texture over the final painting in photoshop. This can be added in the compositor in Blender with a texture set to overlay/soft light/linear light.
But overall, to give it a painterly look, it starts back in the lighting and composition, and trying to replicate the feel of old masters paintings. Aesthetically it’s about light and dark counterbalance, and where you want your eyes to focus on. On top of that, there’s the emotive qualities which need to come across.
Then once it’s rendered, I do a photoshop paintover to add texture, add detail in focal areas, simplify detail in peripheral areas, and breakup, and most importantly, painting over clean 3D edges, which might be much more impressionistic in an old painting. Also, this helps draw focus to the most important parts of the painting. Keeping secondary parts of the image loose and impressionistic, whilst keeping contrast/sharpness/clarity in the main focus points. The photoshop mixer brush with a rough texture is great at giving you this feel.
Then, and only then do I stick the canvas texture over the whole image along with some other post effects such as slight chromatic aberration, grain, and lens blur to make it feel like it’s a photographed painting.
Just sticking a canvas texture on a very cheap looking image will look like just that… a clean cgi render with a texture on top.