Would a non-envelop, prefix only, SHA2 built MAC be susceptible to key recovery attacks?
None of these constructions will lead to key recovery unless the underlying hash function is spectacularly broken in the sense of preimage resistance, which pretty much none of them are (archived).

But key recovery is not usually what's directly relevant to your application.  If you're using one of these constructions as a MAC, for example, what's relevant to your application is forgery—and while key recovery is one path to forgery, it's not the only path to forgery.  In MAC applications, length extension is fatal: it is trivial to forge MACs under $m \mapsto \operatorname{SHA256}(k \mathbin\| m)$.

These days, it's all an academic concern, because:


the world has settled on using HMAC to get a PRF out of SHA-256 so it's ubiquitous and ready at hand essentially everywhere,
there are much cheaper MACs like GHASH and Poly1305 built into authenticated ciphers like AES-GCM and crypto_secretbox_xsalsa20, and
SHA-3 and BLAKE2 natively provide keyed variants anyway with PRF security so you don't need to construct your own—and making the prefix construction secure was an explicit design criterion for the SHA-3 competition if you really still want to use it.