PDFium has their own base/ that they do their best to keep in sync; for that, we'd file a bug against them and let them handle it.
For Blink generated code, we would update the generators to no longer use FALLTHROUGH and regenerate the code.
For third_party, you'll need to go case-by-case and figure out how to do it. For some of them, it's in the integration code and you can just change it in the tree. For others, you might need to change it upstream and re-roll the DEPS. I've done this before, so I can give guidance if necessary.
In the past, I've found it useful to do a burndown. Start with the LSC across Chromium and Blink, and let's see what's left.