Used to commute with a pump, park patch kit, tyre levers and allen keys. But these days, running better tyres, i just have the allen keys incase i need to adjust anything, stop a creaking seat etc…
That said, i do keep on top of my maintenance, clean the bike, chain, gear adjustment if needed at the weekend (if required). It’s very easy to tell if your bike needs lube, gears are out etc… when you ride it every day.
It’s not uncommon for me to lend a hand fixing other commuters bikes on route (used to work in bike shop so confident and safe to do so). The most common problem being a slipped chain, often due to the terrible condition or set up of their bike. Most people in these situations are not dyed in the wool cyclists BTW. Seen a fair few forks the wrong way round, wonky wheels, disconnected brakes, wobbly cranks and massive vs small bikes for the people ridding them. It’s pretty easy to spot someone who wants help and i like to think it helps strengthen the bond within our growing cycling community.