Most unions pay their elected officers and administrative staff. Members might volunteer for some activities but the roles that come with a significant time commitment are jobs like any other.
VFW membership has declined because even with continuous wars for decades, the end of conscription has meant a lot fewer veterans. And many VFW halls functioned more like dive bars than anything else: nothing wrong with that, but not particularly attractive to most younger veterans.
The VFW is just a stand-in for any community "lodge" type organization, all of which have been in decline for decades. Yes, this is somewhat about the "cool" factor -- young people largely don't want to be seen in a Moose Lodge, Elk Lodge, Lions Club, Masonic Temple, etc., and these organizations typically have backwards views on female membership, have racist histories (or presents), etc. -- but the fact remains that, instead of doing this community-oriented thing, people are doing other, market-oriented things. Instead of playing darts at the American Legion, they are paying to go to an escape room, or even just staying home and gaming or shopping on TikTok. Even country club membership is in decline, so this isn't only a working class phenomenon.
I'm not as sure what point you're making about union staff. Surely there has been paid union staff for decades -- no real change there AFAIK -- and being "active" in the union doesn't mean you are doing paid staff work (though part time positions for retirees aren't that uncommon). There's a lot of stuff going in on a truly active union local that is definitely not paid work: being on the committee that builds the 4th of July parade float, organizing the games for the summer member picnic, organizing a group to go work in union colors at a Habitat for Humanity build, putting together care packages for sick members and sending groups to visit with shut-in retirees. You're right that, sadly, few locals are this active anymore, but it was once common.