Is ham ultra-processed?

It depends whether the ham is a piece of meat or a product built from pieces of meat, and that is the whole distinction.

Ham carved from a joint, cured with salt and possibly a nitrite, is group 3. The pork is still the thing you are eating, exactly as with bacon.

Most sliced packs are reformed

Sandwich ham is commonly made by tumbling pieces of pork with brine, then binding and pressing them into a block to be sliced. Doing that needs added water, phosphates or other stabilisers, and often added protein. That is group 4.

• Carved, hand-carved, or on the bone: usually group 3.
• Formed, reformed, or made from ham pieces: group 4. The wording is regulated rather than marketing.
• A declared added-water percentage is a strong signal of group 4.
• Parma, serrano and other dry-cured hams are group 3: pork and salt and time.

This is the category where reading the pack changes the answer most often for the least effort, because the legal wording does the work for you.

Working this out from a receipt is harder than from a packet, because a till prints about twenty characters of product name and no ingredients list. That is the problem Bagged exists to solve, and how a receipt is structured explains why it is the hard part.