Will good quality running shoes last that long? Or will, say, the padding at the bottom lose it's springiness? (I can't tell if it's that, or if it's a bad track, or if the problem is that my knees are older.)
As with food "best by" dates, you can get away with rather a lot more than they recommend. But a quarter-century seems like too much to ask.
Conventional wisdom is running shoes will last about 300-500 miles but this is not a concrete rule. The insoles will form to your feet and lose springiness and support. The soles will wear down reducing traction and lose support.
I tend to wear down the topsides around the outside forefoot and big toe area and the materials starts to tear.
It's not really a problem, per se, to run in old shoes but the experience will likely be better with new ones. Technology and materials get better, lighter.
I think a proper fit matters more than new/old. My oldest pair of shoes I still wear are from 2006 (Birkenstock Boston)
Good luck, running is high impact and best to run on trails/dirt/grass when ramping up again rather than pavement.