I want to achieve the speckled black dots around the image and text alongside the overall rough texture on the shapes. Tried using spatter and texture overlays however I can not achieve the desired texture of the below image. Fully aware that this will have been printed and rescanned afterwards
The basic paper texture can be made using a layer above with any paper-like texture as a grey (rgb 128 128 128), and then set the layer blend to "difference" with a low opacity.
The fuzzy edges from ink bleed, you might try using "color range" selection with a high fuzziness on the ink, dupe that to its own layer directly above the drawing layer and then play with blur and/or texture tools. Then leave that to overlay the original drawing with low opacity.
The sample looks like an actual drawing where the artists' hand and arm was touching the paper and has smeared the ink. You can try using smear tools to imitate this on a local basis on a duplicate drawing layer under the original drawing layer, with a color adjustment. Maybe start with a basic blur tool first.