On my MBP5,2 mid 2009, auto gpu switching I never used. As for manual switching, it was cumbersome in Catalina: change it in enery saving, then log out, reboot, and the new GPU setting should stay. Didn't always work, and in general the system behaved better with the 9600M GT GPU. In Mojave, was quite unstable across sleep/wake with the 9400M.I can’t really can’t remember because I haven’t used an 09 in a hot minute. What I do remember though is the option to switch gpus was under energy saver under El Capitan but I’m not sure if it’s under there on Monterey or Big Sur. I remember it would give you two options like energy saver and performance mode and it would then make you log out. Also it’s kind of strange that gfxstatus isn’t working.
Trying to switch with gfxCardStatus didn't have an effect, as you observed as well.
In BS and Monterey, gfxCardStatus also doesn't work. When I thought I have to switch, I booted into El Capitan, switched there, then after booting back the new setting persisted.
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