This is actually a very interesting question. I assume that you are referencing extensions that add shards to Postgres, since it runs on a single server out of the box. You made me curious how those extensions/rewrites handle sequences.
It looks like Citus (one such extension that runs shards on separate workers) does something a little like what you described. Each node gets an ID, which becomes the high bits of the sequences it generates. So serial IDs are monotonic within a shard, but not across shards.
Aurora PostgreSQL Limitless uses different abstractions, but also ends up reserving different chunks of IDs for different routers to use.
It looks like Citus (one such extension that runs shards on separate workers) does something a little like what you described. Each node gets an ID, which becomes the high bits of the sequences it generates. So serial IDs are monotonic within a shard, but not across shards.
Aurora PostgreSQL Limitless uses different abstractions, but also ends up reserving different chunks of IDs for different routers to use.