Repairing inside permanent shelving of kitchen cabinets.

We have 30 year old oak exterior, white melamine interior kitchen cabinets. (Will be sanding and restaining the oak exteriors). The interior shelving is white melamine over particle board, that have disintegrated edges from wear and water damage. Looking for ideas to repair these edges. Am also thinking of 2 or 3 coats of primer (not paint) to spruce them up on inside, however, concerned about primer peeling or sticking to dishes. Anyone out there tackled these 2 issues on white melamine shelving?

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