HMAC-SHA-256 vs SHA-512/256 vs truncated SHA-512 for use as a MAC
Option 2 and 3 are appropriate for a MAC, assuming the length of the key is not variable (otherwise appropriate padding must be used, similar to that used in KMAC). In this manner, it behaves like SHA-3 which does not need to be run in the usual nested HMAC construction. Numbers 2 and 3 are actually virtually identical. The only difference is that SHA-512/256 uses a different IV than plain truncated SHA-512. They all provide protection against length extension attacks.

Note that you can optimize HMAC to reduce the number of calls to the hash. Any decent implementation will not have significantly impaired performance compared to HMAC-SHA-256. You can also get away with only executing a single SHA-256 function using an older construction called an envelope MAC which concatenates the key, message, and key again, with padding.