I like BLAKE3 just fine. Nobody's really going to ding you for using it (or SHA3 for that matter). But it would not be sound practice to tear SHA2 out of a system that was already using it.
Two other notes:
(1) The article explicitly recommends HMAC-SHA2, not SHA2 by itself.
(2) Where it does recommend SHA2 directly (for hashing, not authentication), it recommends 512/256, which is truncated and can't be length-extended.