Einstein spent his later career trying to reconcile general relativity and quantum mechanics. He failed. So has everyone after him. It's not about Einstein being old. It's that it's a really hard problem.
It should be pointed out that the math of spinning black holes which Einstein needed to reconcile GR and QM wasn't discovered/invented until the 1980s. And we still haven't really checked to see if he was on to something. A big part of this is that the young have the energy to spread their ideas. The old often don't. That has as much to do with these things as being right or "on to something".
Not a physicist, so this may be a dumb question… but do we even know for sure it’s a problem with a solution?
This is my understanding as well. What the article described has been cannon for almost a century, but it may not be an accurate representation, and we still don't have the answers to address Einsteins' concerns.
(Article quote in question: "But toward the tail end of Einstein’s life, he argued strenuously against the concepts undergirding the emerging field of quantum mechanics, the ideas that are shaking up physics yet again and may lay bare even more of our universe’s mysteries.")
TFA also refers to just Einstein's 1905 papers. He published general relativity 10 years later. And after GE he contributed e.g. stimulated emission, Bose-Einstein statistics, Einstein-de Sitter cosmological model and the EPR paradox, among lots of other stuff.
Also the claim "toward the tail end of Einstein’s life, he argued strenuously against the concepts undergirding the emerging field of quantum mechanics" downplays that Einstein was pivotal in emerging the field in the first place.