The client lists algorithms (zlib = 1, brotli = 2, zstd = 3); the server sends a CompressedCertificate message instead of Certificate. Chrome and Safari advertise brotli, and Cloudflare, Google and other large sites compress their chains. Savings matter because the chain often dominates the server's first flight and can push it past the initial congestion window, costing a round trip.
Compression cannot rescue post-quantum signatures, which are random-looking and do not compress; that is part of the motivation for Merkle Tree Certificates and for omitting intermediates that clients already have.