Phone cameras usually don't have a defined focus position. When you take a picture, the camera always has to focus again through the whole focus range. This makes it impossible to do focus stacking. Correct me if I'm wrong or if there are exceptions.
The cheap microscope USB cameras have either a chip that is placed somewhere down the tube or a lens that projects from within the tube on the chip.
In case A you get a small cutout of the picture your objective places in the tube. In case B you can be shure that this lens won't know what your objective is and what correction it needs. My impression is that you can get so-so image quality from these cameras, but the images with really great technical quality are made with more complicated equipment. Your phone is probably a lot better. BTW does you phone offer raw image capture?
For really great image quality you can either buy a special camera for impressive sums of money or you can use a well chosen digital camera.
Important point for this choice are:
- EFSC (electronis first shutter curtain) - vibrations are a much bigger problem in micro-photography than elsewhere
only few cameras offer this: A couple of Canon DSLRs, very few other DSLRs, Sony A6XXX, NEX7 and some others, Nikon One, to some degree some Olympus MFT cameras, some Panasonic MFT cameras
- suitable optical system (eyepiece, relay lens if needed... no plastic lenses in this system!) often these parts are rare and expensive
- suitable ergonmics (tiltable display, thethering to phone, tablet, notebook)
- sturdy and adjustable mechanical coupling (what size is your lathe?
You can see that it is not simple and cheap to go beyond what your phone camera offers.