Can you shut the vanity hot manifold valve off, disconnect that hose, and hook it to an auxiliary or other functioning manifold outlet, and see whether the debris issue halts. That’s a step in tracing back to see which part of the vanity’s line is collecting stuff it shouldn’t. It may be no easy task to get at or remove a manifold hose, though. I’d expect the source to be between the manifold’s vanity hot valve and the faucet. Hot lines seem to collect stuff more than cold, if washing machine screens are any example.
Additionally, in case that vanity is farthest from the manifold and maybe acts as an “end collector”, shut that valve off and see if debris shows up then at another faucet. Something originally an aberrant part of the system may have sluffed off and lodged along that section.
I dunno, I’m shooting in the dark, huh; but this is one of those confounding head scratchers where reasoning seems helpless. 😵💫
Joel