Your new standard should be Ed25519. ;)
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Size of key isn't directly comparable to RSA. Both kinds of keys are structured rather than fully random values. RSA 3072, P-256 and ed25519 are all offering approximately 128-bit security in terms of random symmetric key size. Key sizes for asymmetric encryption are misleading.
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Yeah, that's what I said: ed25519 only has a single key size, 256-bit, and offers approximately 128-bit security just like P-256 and RSA 3072. As long as the key is encoded efficiently, there's no reason to expect it to be long. It's 64 bytes as binary, bloated a little as text.
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Signatures are 512-bit (128 bytes as binary) so it's really lean. ECDSA P-256 has the same sizes. Bitcoin acts as a massive bug bounty for ECDSA sec256k1 which has the same key size too. Anyway, asymmetric keys are usually used to bootstrap symmetric encryption.