How secure is using a hash function as Key Derivation Function?
This is reasonable as long as (a) you mean some unique encoding of the seed and index $y$ when you say seed + y, (b) you never use the same seed and index for another purpose, and (c) you chose SHA3-256, or SHAKE128-256, or SHAKE256-256, and you are using the standard Ed25519 32-byte pre-master secret seed as the secret.  For (a): if, e.g., the seed is always exactly 32 bytes, you can use concatenation.  If the seed may vary in length, you might consider concatenating $n \mathbin\Vert \mathit{seed} \mathbin\Vert y$ where $n$ is the number of bytes in the seed so that there are no pairs of $(\mathit{seed}, y)$ that might be confounded by concatenation.

Note that the answer is specific to the SHA-3 functions above.  This does not apply to everything that might be called a hash function.  It is certainly not true of GHASH.  It doesn't even apply to SHA-256 unless you impose the additional constraint on the seed and the index that their lengths each be fixed, or that their encodings be length-prefixed.  This is because given $h = \operatorname{SHA256}(\mathit{seed} \mathbin\Vert y)$, it is easy to compute $\operatorname{SHA256}(\operatorname{pad}(\mathit{seed} \mathbin\Vert y) \mathbin\Vert y')$ without knowing the seed—the standard length-extension attack on SHA-256.  If you must use SHA-256 with variable-length seeds and indices (which it sounds like you needn't, but other passersby might read this), it may be simpler to just use it with HMAC to make a PRF, if not HKDF.

Generally, you should consider using something tailored for the purpose unless you have constraints ruling it out: KMAC, if you want a Keccak-based PRF; HKDF, if you must use SHA-2 and you want structured inputs for application and purpose labels.