Why didn't Sirius, and Ron, Harry, Hermione just conjure animals to use as food while they were on the run?

I know, I know, Gamp's Law of Elemental Transfiguration!... but hear me out.

I am aware that food cannot be produced out of thin air. However, I just realised, there seems to be some sort of exceptions to this law. Serpensortia produces snake out of thin air! That seems strange to me, given the above law. I know snakes aren't exactly considered food in many parts of the world, but there are plenty that do.

Also, Hermione seems to be able to conjure canary out of mid air too. Book 6:

He found her in the first unlocked classroom he tried. She was sitting on the teacher’s desk, alone except for a small ring of twittering yellow birds circling her head, which she had clearly just conjured out of midair. Harry could not help admiring her spellwork at a time like this.

Furthermore, she seems to have some control over the conjured birds; Book 6:

“Oppugno!” came a shriek from the doorway. Harry spun around to see Hermione pointing her wand at Ron, her expression wild: The little flock of birds was speeding like a hail of fat golden bullets toward Ron, who yelped and covered his face with his hands, but the birds attacked, pecking and clawing at every bit of flesh they could reach.

And then, we have plenty examples of transformations of objects into various animals.

Seeing as how snakes and birds can be conjured from thin air, there must be a way to conjure other animals as well, right? (I can't think of any examples where this happens in the books right now, though)

Why did Sirius Black, in book 3, go days and possibly weeks starving and eating out of trash cans when he could have just conjured a chicken or a rabbit out of thin air, ordered them to stay still and humanely kill the animal and conjure some fire and cook the animal and eat? Even if you can't conjure rabbits, Freshly cooked snakes and birds would surely be better than food scavenged from the bins, no?

Same with our favourite trio: Ron, Hermione and Harry. When they are on the run from the death eaters Ron constantly complains that they always have the same thing to eat (was it fish?). Surely, Hermione is clever enough to figure out that she could conjure animals, instead of wasting time hunting and fishing?

How does conjuring animals work? Why doesn't the Gamp's law apply in this case? Why didn't anyone think of conjuring animals for food instead of fishing / hunting / scavenging / starving?

Answer

They probably wouldn't have been edible

There are indeed many examples of people conjuring apparently edible things out of thin air. You mention the animals that Hermione and Draco conjured, but there are plenty of other (apparent) examples. For example. Mr. Ollivander conjured flowers out of Fleur Delacour's wand, which could potentially be edible:

Mr. Ollivander ran his fingers along the wand, apparently checking for scratches or bumps; then he muttered, “Orchideous!” and a bunch of flowers burst from the wand tip.

—Harry Potter and the Goblet of Fire

However, as indicated in this answer, it is possible that conjured objects will disappear after a short while, making them rather useless as a form of nutrition.

In addition, this answer suggests that conjured objects may have the appearance of edible food, without being nutritious per se.

Let us remember that Gamp's Law is mentioned in the context of explaining why the apparent conjuration is food is merely apparent. As such, looking to explanations like these seems prudent.