I doubt that people have replaced gas caps often enough to have experimented with aftermarket ones. A poorly sealed gas cap on my 2014 caused the CEL to illuminate which caused the adaptive cruise control to stop working something like 3 years ago. I was on a 400 mile trip so I pulled off at an exit and removed and reinstalled the gas cap. The CEL went off after driving a while but I don't remember how far. As soon as I noticed the CEL was off, I found that the cruise control again worked. I don't know if the gas cap really needed to be replaced but I bought a new one as soon as I got home since I was pissed about not having cruise control for 50 miles or so of the drive. I've since been more careful to tighten the gas cap fully after refueling.
What dash lights are not shutting off? It was only the CEL illuminating on mine and it turned off by itself not long after removed and reinstalled the original gas cap.
It's not just the Sienna that a poorly sealed gas cap causes problems on. It can happen on lots of makes and models. .
Edit: Does the opening of the fuel filler pipe appear to be OK ... e.g. no rough edges that could be preventing the filler cap from sealing? OEM gas caps should last for years - not days.
Edit 2: Could something else be causing a loss of pressure in the fuel tank? Could the filler tube be damaged or rusted? For example, the fuel filler tube on a Honda Accord my wife used to drive rusted through after about 8 years.