There is an exemption to even SYL and loading restrictions, but whether it applies depends on the facts.
Elderly father (late 80s) take the grandkids to our local park with my sister Sunday morning. He displayed a valid blue badge on the vehicle but didn't see/realise.
So, was the car parked and all occupants disembark to go to the park for a period?
Looking ahead, as the car is 2026 reg it could be leased or hired, so it's necessary to ask who is the registered keeper and are their DVLA details current.