Do the Guitar Hero World Tour instruments work with Rock Band 2, and vice versa?

Rock Band 4 Wireless Guitar Bundle - PlayStation 4 : Mad Catz: Everything Else

Guitar Hero World Tour vs Rock Band 2

Official Guitar Hero/Rock Band Instrument Compatibility Chart

PS3 Rock Band Bundle: The Beatles and Rock Band 2 (Sony PlayStation 3) Complete

Rock Band 3 - Wikipedia

Sony fixes rhythm: all controllers to offer “basic compatibility”

How John Mayer conquered the world

Rock Band in 2023: FAQ (Instrument Availability, Compatibility, Exports, Legacy Games, and the Future) : r/Rockband

compatibility: did you guys know if guitar hero warriors of rock is compatible with the guitar hero 3 guitar? (see pic, Wii version) : r/ GuitarHero

PS3 Guitar Hero GAME SERIES - Legends of Rock World Tour Metallica Warriors etc

Rhythm game accessories - Wikipedia

Are the rockband foot pedals compatible with all console drumsets since they just plug into the drum? - Quora