I did some research on this and basically most sources indicate that as long as the SRS light is not illuminated, the airbags are still passing their internal checks. That doesn't mean they are guaranteed to work, but the electrical portion at least still passes its checks. Solid fuels of this type are frequently able to still function normally several decades after manufacture but ask anyone who picked up a 50-year old box of rifle ammunition at a surplus sale and they'll probably tell you about how 1 out of every 50 rounds or so simply won't fire or else misfired and either left the bullet in the barrel or having left the barrel at far lower than designed velocity.
I have a 1997 car and am far more concerned about the fact that crash structures and crumple zones on cars from the 90's were horrible compared to modern cars. This is especially true of economy cars, which is exactly what mine is and you're basically guaranteed injury or death in a 90's car if you get in a crash equal to the partial or small overlap tests they run now, which simulate various types of real-world collisions. It's actually pretty rare in the real world for two cars to collide 100% head-on with total overlap. The partial overlap crashes are much more common and a lot harder to survive in cars from before 2005 or so.
For me, I mitigate a lot of the risk by simply not driving much. Driving risk is measured on a per-mile basis and actually it is measured to be higher risk on weekdays, during rush hours, and overnight. I do my best to eliminate as much driving as I can as well as to avoid the high risk periods. Maybe in another 6 months to a year I'll replace my car with something safer and with modern features like heat & air-conditioning, neither of which does my car have.