they definitely last longer

for most of them it's not necessary for food safety but prolongs their shelf life. an uncut bell pepper will last a few days at room temperature but weeks in the fridge

for cut up vegetables, refrigeration is pretty much mandatory because by cutting them you've inevitably spread microbes all over their soft vegetable interior tissue that was previously protected by an outer skin (e.g. pepper, tomato)

that's why I prefer single serving size tomatoes like cherry or grape tomatoes, because they don't take up fridge space. but they're more expensive :[

bonus info: if you get a UV lightbulb you can blast the outsides of the vegetables with it to kill off most microbes. that's how I get my peppers to last sometimes as long as 1.5 months in the fridge. can't grow mold if all the mold died :]