I’ve used Stitch Fiddle in the past to create designs from an image (although I’ve only made a few patterns myself). The site also has a “draw line” feature so you can add in your backstitching. They do have a download your project feature, but idk if they give pdf as an option.

I do find their designs require a little tweaking tho since they add a bunch of colors/gradients along the line edges. To do this I basically just delete or reassign the unnecessary colors to the main color. That way I don’t have to manually edit each pixel and the process isn’t too tedious.