Is a ptrap necessary for a soft water system in the garage to prevent clogging from hard minerals and brine buildup?

If you’re connecting the discharge directly to your sewer line, then yes, you need a p-trap between any fixture and the sewer line. It should also be vented to prevent water from being siphoned out of the trap. If the code allows, you can use a studor vent. Water softener discharge is in solution, so there shouldn’t be any clogging issues. If you’re discharging into an existing floor drain connected to the sewer line, the floor drain will already have a p-trap. If you’re discharging outside with no connection to the sewer line, then no trap is needed