It varies across clients, but most clients will read/write the relay list they use. As with most things though, there are two standards; an old-hacky stringified-JSON in the follow list, and the more modern approach of using event kind 10002 to store read and write relays.

This latter is (one of the) key pieces of the puzzle that we call “outbox model” (formerly gossip) - which is how a client knows where to read/write for specific pubkeys and is one of the key aspects that makes nostr credibly censorship resistant.

 We also have a NIP (87) for client-specific configurations which can serve as the basis to, for example, copy someone’s configuration of a particular client.