That is some type of polypore, aka shelf mushrooms, some get very woody and can last a year or more after they grow and dry out. Maitake and chicken of the woods are in the same family, and a few others are edible when young but I’ve never tried them. Dryad’s saddles are pretty cool and really common around here but the smell puts me of. Same with Black staining/Berkley’s polypore. Then there are medicinal ones like reishi, you can draw on artist’s conks, and star fires/make hats with tinder fungus. There are no poisonous polypores from what I’ve read, so it is a very safe and distinctive group to forage. edit: there are a few poisonous ones after all, it seems folk wisdom didn’t account for polyporic acid.
Oysters are very delicate, and fungus gnats love them so they rot soon after their prime. I find a type that fruits irregularly in the summer around here, always on tree/ logs that still have some bark. There is another mushroom called angel’s wings that is very easy to confuse with oysters and can be deadly to people with kidney problems.
Audubon makes a good guide, and there are great online resources like mushroomexpert.com to learn more about specific species.