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/core/tests/suite/rmcp_client.rs

@@ -1808,7 +1808,7 @@ async fn streamable_http_tool_call_round_trip() -> anyhow::Result<()> {
     .await;
 
     // Phase 2: start the Streamable HTTP MCP test server in the active
-    // placement. In full CI this may be the remote executor container; locally
+    // placement. In full CI this may be the remote environment container; locally
     // it is a host process.
     let expected_env_value = "propagated-env-http";
     let Some(http_server) =