I still think the only thing that makes sense is to make Short Rests = camping supplies. Otherwise, like Tuco said, what's the point of even automating it or even having the mechanics at all?
If I can Send to Camp automatically and then use everything I Send to Camp for Long Rests, then why bother at all? I never have to carry around camping supplies. They just get thrown into camp and then I can just use them whenever I want. So why have food at all? Why not just cut all food from the game?
The only thing I could come up with was that you might need to have food on you in order to short rest. So, you might send most camping supplies to camp, but you might need to save enough and carry enough on you to short rest if you want to take advantage of the benefits of short rests. Then, you would have to weigh the cost of keeping it on you with how much do you want to be able to short rest.
So, Short Rest = 1 Camping Supply per Character Level per Party Member traveling with you. At level 4, that would be 16 Camping Supplies per Short Rest. At level 6, that would be 24. Not a huge price, and you'd have a legitimate reason to actually keep Camping supplies on you.
Long Rest should then = 2 Camping Supplies per Character Level per Character at your Camp. So, if you are level 4 and you have the MC, Gale, Shadowheart, Astarion, Wyll, Lae'zel and Volo at your camp, that's 2x4x7=56 Camping Supplies per Long Rest.
This gives you also a reason to maybe just chuck characters you maybe don't think you'll need or want instead of just leaving them at camp forever. If you know that it'll cost you more Camping Supplies to keep Lae'zel around, and you can't stand her anyway, ask her to leave so you don't spend as many Camping Supplies per long rest. Don't like Volo, ask him to go. Don't like Halsin, tell him get lost. (Withers wouldn't count since he's undead.) Scratch might cost half that, and the owlbear cub also half that (or maybe even a quarter.)
Then, make difficulty settings so that the harder the difficulty the less food you actually find in the game. Suddenly, Camping Supply management becomes a challenging element and not just a "what is this thing here we don't really need?).
And take away the whole limit to Short Rests. If camping supplies are your limit, then you don't need to limit 2 Short Rests. If you have enough supplies to short rest several times a day, that's great. Good for you. However, if you foolishly spend all your Camping Supplies using short rests, and suddenly you don't have enough to long rest, then you are going to struggle until you find more camping supplies, or you go to a merchant to buy more. Thus, it makes it more valuable that merchants sell them as well. If you mismanage them, you still always have the option to spend money to buy what you need so you can long rest.
This puts more of the management of camping supplies on the player to manage wisely, and it limits short and long rests better and gives you a reason to not send all camping supplies straight to camp.