Too Long/Didn't stop writing...
Platypus bags roll up nice and small for storage and fit in most water bottle holders or even loose in the pack. In hot or cold temps walking you'll use (should be using) a -lot- more water than normal, there's a balance between carrying too much and too little, particularly if there are good sources enroute, but every stop to fill up is time, time is speed, speed is safety. You can always lighten the load by drinking it.
Depending on your particular situation there's nothing "wrong" with having some redundancy.
At work you might keep a more comfy "shelter-in-place" kit which doesn't need to be light, mobile, or particularly "survival specialized" so can be dollar store type household stuff: blanket, toiletries, change of clothes with decent shoes -shoes are always key, learned that from any number of movies
-, some basic meds and any specialized ones, spare glasses/contacts, water purification, some comfort geedunk (including the aforementioned C2H6O), and maybe even some drink mixes and canned or dehydrated food and a cheap way to prep and heat them. The .gov's 3-day kind of stuff. If you have the training and can afford it or get it bought there's no reason not to have the company first aid kit go beyond aspirin and bandaids into trauma stuff. You aren't paying for the lease to store it after all.
Keeping a small, light, basic "EDC kit" with you at all times on your person is never a bad idea. Small knife, light, fire-making, button compass, multi-tool, etc.; the classic Altoid tin-type survival kit contents, even if on keychains and distributed through pockets. For me, living in a city and having other supplies elsewhere, I'd go with more emphasis on things I'd actually find handy day-to-day like bandaids and pain-killers, first aid stuff. Don't have much need daily for a survival snare or fishhooks.
As you get more stuff you can maybe build out an EDC "bag" as discussed with a real get-home kit in it to take on the job or leave in your car.
Your car should already have the makings of a car-specific comfy "shelter in vehicle" kit (with carrying capability, like a folded seabag with straps so you can switch it all easily and quickly from transpo to transpo, IMO). More serious first aid trauma type kit and the training to use it (also handy for range trips), blankets (picnic anyone?), spare seasonally-appropriate clothes/shoes (the Splash Zone at Sea World is a great idea, til the sun goes down and you're still wet), candles, fire-making, nice soft TP, basic ingress/egress tools and duct tape (my robbery/rape kit, as it'd be called in NYC). Add water-purification, water storage and maybe some chow. Flares, shovel and chains for snowy climes, esc.
Whenever I read of some idiot dying from exposure, cold or heat, because their car got stuck for a few days I can't muster any sympathy, the basics are responsible car ownership 101.
The one thing I notice a lot of people leave out of all the above "kits" are spare vision and meds. If you can't see, you just increased your degree of difficulty a hundred-fold. If you can't treat your chronic ailments you might just die. Spare ugly framed glasses are comparatively cheap, even your last prescription should be "good enough".
Weapons and ammo are up to the individual and their laws and situation.
I keep a USB cord, USB car plug, and USB wall plug charger "set" for my phone at home, at work, in my car, and in my briefcase. The parts are cheap on Amazon, you should never have to worry about powering up your phone in a "non-collapse of the grid" situation, the back-up power units and solar and crank chargers are for that. The phone is still a pocket computer with on-board app goodness (if prepared ahead of time) even without signal after all.
