Local symmetries (gauge symmetries) in field theories and general relativity give rise to associated Noether charges or superpotentials, often localized at boundaries or formulated via Noether's second theorem.
The retrieved papers provide robust support from multiple theoretical and mathematical physics perspectives (such as Noether's second theorem, gauge theory, and general relativity) showing that local symmetries do indeed give rise to Noether charges, fluxes, or superpotentials.