The thread title calls for things that are "with you", not necessarily "on you". In that spirit some thoughts:

I agree on the knife, but a prybar or mechanical lever seems nearly as useful.

Heavy-duty gloves ought to be there somewhere.

I don't do the bandanna and do an N95 mask instead. I wear a vest and have room for a 3M folding N95 on my person but don't carry it since I'm concerned that constant flexure would harm the mask.

Goggles? If I don't want to breath it I probably don't want it in my eyes.

For some people keeping a set of safety footwear at work may be a good idea, i.e., something you'd wear walking across debris-strewn concrete, soft mud, and anything in-between.

This may seem excessive but I have a cheap AC voltage detector in the safety kit. If there's a bad storm that knocks down wires I can safely tell if they're live.

PS. I sure seem fixated on body protection. I should probably start with a list of firefighter's gear and work back to practicality from there.