Migrate exec-server remote registration to environments (#23633)

## Summary
- migrate exec-server remote registration naming from executor to
environment
- align CLI, public Rust exports, registry error messages, and relay
test fixtures with the environment registry contract
- keep the live registration path and response model consistent with
`/cloud/environment/{environment_id}/register`

## Verification
- `cargo test -p codex-exec-server
remote::tests::register_environment_posts_with_auth_provider_headers
--manifest-path /Users/richardlee/code/codex/codex-rs/Cargo.toml`
- `cargo test -p codex-exec-server --test relay
multiplexed_remote_environment_routes_independent_virtual_streams
--manifest-path /Users/richardlee/code/codex/codex-rs/Cargo.toml`
- `cargo check -p codex-cli --manifest-path
/Users/richardlee/code/codex/codex-rs/Cargo.toml` (still running when PR
opened; will update after completion if needed)

codex-rs/exec-server/src/process.rs

@@ -24,7 +24,7 @@ pub struct StartedExecProcess {
 /// stdout, stderr, or pty bytes. `Exited` reports the process exit status, while
 /// `Closed` means all output streams have ended and no more output events will
 /// arrive. `Failed` is used when the process session cannot continue, for
-/// example because the remote executor connection disconnected.
+/// example because the remote environment connection disconnected.
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub enum ExecProcessEvent {
     Output(ProcessOutputChunk),