Yes they absolutely care and have been doing serious work to migrate PKI to PQC.

This was the first of several articles coming out of Google: https://blog.google/innovation-and-ai/technology/safety-secu...

And the timeline for web migration is 2027 Q1: https://security.googleblog.com/2026/02/cultivating-robust-a...

And this was Sophie Schmieg’s talk at a cryptography conference this month (they lead PQC migration efforts at Google) tracking migration efforts and urging folks to prioritize signature migrations in lieu of accelerated quantum timelines: https://westerbaan.name/~bas/rwpqc2026/sophie.pdf