A noble quest, but no simple answers and not many cheap ones for the lightest. I applaud your desire to simplify your kit by one less item, but I’ve never been able to make it add up weight wise, not to mention practical use and cost. I did the drill on this, looking for something on the survival side of things and landed on the 40oz stainless H2Go bottle stuffed full of essentials. In practice you could stuff your pockets with the essentials and have a fireproof pot to cook or sterilize water, as well as hauling water (the lid is removable). There’s nothing much UL about that and it won’t be easy to handle.
Options:
Vargo makes a Ti 650ml water bottle that looks much like a Klean Kanteen that is 3.9oz and $85 retail.
Vargo also offers the Bot Ti wide mouth bottle that holds 1 liter, weighs 4.7oz and retails for a wallet numbing $100 (weights are advertised, not verified). Both suffer from being tall and narrow (read unstable in a fire) and require some method of handling them. Try picking up a full one liter Nalgene with a typical pot grabber– weak at best and even more interesting when surrounded by flames or hot coals.
I got a bunch of samples from my gear locker for comparison:

Top row, left to right:
Nalgene Oasis Canteen, 1 liter, 4.6oz
Talking Rain bottle, 1 liter, 1.8oz
“Rocket bottom” soda bottle, 1 liter, 1.2oz
Smart Water bottle, 700ml, 1.0oz
Nalgene UVPE bottle, 1 liter, 3.8oz
H2Go stainless bottle, 1.18 liter (40oz), 6.4oz
Klean Kanteen, 800ml, 8.4oz
Klean Kanteen 1.18 liter (40oz) stainless bottle, 10oz.
Bottom row:
Platypus bladder, 1 liter, 0.8oz
Stoic titanium pot, 700ml, 3.8oz
Snow Peak bowl with Four Dogs lid, Trangia pot grabber, 640ml, 3.8oz
IMUSA 10cm pot with lid, 650ml, 2.8oz
The Platypus and the IMUSA pot win this one and are far more adaptable than the Vargo options. I would use the rocket bottom soda bottle and Stoic pot for a light but practical option. If you want to save space they will nest loosely. You can go light, but at some point you have to use this stuff. After climbing switchbacks all day, you want to eat and not scald yourself or spill your meal.
For a “nearly no-cook” kit I came up with the combination of a MSR Titan mug, Ti Esbit stove, aluminum flashing windscreen, folding spoon, mini lighter, and a screw top aluminum can for fuel. 5oz total and it packs small. That is good for hot drinks, soup, oatmeal, etc.

I forgot the Oilcamp hard anodized aluminum space saver mug. It holds 750ml and weighs 3.6oz and has long handles that would be good for fire cooking. You can get them on eBay for $14 or so. Note that the mug plus the Platypus is a hair less than the $100 Vargo Bot. The rocket bottom soda bottle plus the Oilcamp weigh 0.1oz more and costs $86 less!

Left to right: Olicamp hard anodized Space Saver mug, Stoic Ti pot, Oilcamp clear anodized (don’t buy the clear anodized model).