After more testing, I can confirm that: no, mining strike speed is not different between Tauren and HM Tauren – Each strike takes roughly .8s to complete.
A regular tauren gathers a mining node in three strikes, and almost finishes a fourth, which takes 3.2s.
A HM tauren gathers a mining node in three strikes exactly, taking 2.4s.
And to be extra certain: I tested it on live this time, on copper ore rather than Dragonflight ore. The HM Tauren racial is indeed working and reducing gathering times for mining nodes by 25%.