Fate (any edition) is not built to handle nitty-gritty details. You can, of course, add and respect those details, but Fate won't help you much there.
What it excels at is abstracting those details to the "story pressure" level. Fate does not tell you how many cans of sardines you have left. It tells you if food is becoming a problem, and lets you tell why.
If you want to emphasize tools and supplies in a survival game, the bronze rule is your friend. Yes, it was codified in Fate Core but many Fate veterans have been doing the same thing before Core. It is compatible.
For a survival game, I'd put forward two separate methods. One for tools, another for supplies.
Tools & Equipment
The typical way of using aspects could work here. The group could have a communal set of aspects for T&E, or everyone could have one or two of their own. Remember that aspects are not only for invoking. They are "always true". They can be used to justify actions without providing bonuses. It also helps to clarify that these T&E aspects would have less plot immunity than regular character aspects. They are subject to removal if the plot warrants it.
Maybe I'd go a bit further and make the T&E aspect slots as a kind of anti-consequence slots. As a player, you mitigate stress or get a bonus to your roll by filling in an empty consequence slot. This could work in reverse; you start with your T&E slots filled, but sacrifice and cross them out for mitigating stress or getting a bonus. Just like consequences, you could have different values on them like Minor/+2, Moderate/+4, Major/+6 and maybe Critical/+8.
It should also be possible to find, buy or jury-rig new equipment during play, but these would be temporary aspects with zero plot immunity unless the players choose to use an available T&E slot for them.
This is somewhat simpler. Stress tracks are perfect for representing a dwindling resource. Just define one or more shared stress tracks for the group, and attack them daily and when the story warrants it. You could just define a general-purpose "Supplies" track, or you could give it more detail by defining separate tracks for "Food", "Water", "Ammo", "Fuel" etc…
One caveat: keep in mind that these stress tracks do not represent days-worth-of-food or kilometers-worth-of-fuel. They represent how much of a problem these resources are at any given moment. You narrate the details on the spot.
Don't limit your narration to the lack of the said resource. Maybe you have lots of beef jerky, but one of the characters is vegan. Maybe there's a pristine stream flowing, but you only have one bottle to fill, so you can't stray too far from it. Create tension and hard choices.
These stress tracks are in an ongoing conflict with the environment, so they only clear when the characters get a chance to resupply.
And if the group is taken out on one of these tracks, related bad things happen as narrated by the GM, as usual.