Whether a remodel needs a plumbing permit is decided by the city or county building department for your address. Plan on one when the job moves or adds water, drain, vent, or gas lines.
The standard is statewide. Utah's State Construction Code adopts the 2021 International Residential Code, the 2024 International Plumbing Code, and the 2024 International Fuel Gas Code, with state and local amendments, as the standards for building construction, alteration, remodeling, and repair (source). Local building departments issue the permits and do the inspections.
Salt Lake City, for example, says no one may make any installation, alteration, or improvement to the plumbing system in a building without first obtaining the prescribed permits (source).
The permit is pulled before the work starts. The inspection puts a second set of eyes on drains, vents, and gas lines that no one will see again once the tile is up.