But what does "verified" actually mean in this context? And why is the "sup m3" variant so critical?

(Custom Firmware). This is the most popular way to unlock better performance, more emulators, and a cleaner interface. Verified Firmware Options MiyooCFW (v1.3.3 or Beta 2.0):

or more; do not turn off the device until the screen goes black or the menu appears. Key Performance & Compatibility Notes Hardware Variants

A version means the file has been checked against a known good hash (an MD5 or SHA-1 checksum) provided by the original releaser or a trusted moderator from a preservation site (like Internet Archive or GBAtemp).