I'm lucky I don't live far from my favourite beach and, as I love an early morning run, I tend to leave my house key in a hidden place at home. I wear the absolute minimum - shirt, shorts and shoes - and leave these hidden by a rock. This leaves me free to jog along in the nude. So far (touch wood) they've never been disturbed.
The shirt is probably not necessary.
I've never had a concern about leaving stuff on the sand, even if I/we go on an extended walk, swim or paddle. Aussies always seem to just keep an eye on neighbouring stuff on the sand while the owner is off enjoying time away from their spot.
The keys and phone will be on the towel but out of sight, usually under clothing or at least a folded corner while the kayak trolley has always been where we left it. Depending on the location and whom I'm with, I may sometimes have a shirt and shorts or sometimes just my swimsuit and an obligatory hat. Perhaps a bag to carry a snack, drink, sunscreen and book for longer stays. The minimalist option is a sarong which doubles as a cover-up for the non-CO zone and something to lay on.