[MCP] Add experimental support for streamable HTTP MCP servers (#4317)

This PR adds support for streamable HTTP MCP servers when the
`experimental_use_rmcp_client` is enabled.

To set one up, simply add a new mcp server config with the url:
```
[mcp_servers.figma]
url = "http://127.0.0.1:3845/mcp"
```

It also supports an optional `bearer_token` which will be provided in an
authorization header. The full oauth flow is not supported yet.

The config parsing will throw if it detects that the user mixed and
matched config fields (like command + bearer token or url + env).

The best way to review it is to review `core/src` and then
`rmcp-client/src/rmcp_client.rs` first. The rest is tests and
propagating the `Transport` struct around the codebase.

Example with the Figma MCP:
<img width="5084" height="1614" alt="CleanShot 2025-09-26 at 13 35 40"
src="https://github.com/user-attachments/assets/eaf2771e-df3e-4300-816b-184d7dec5a28"
/>

codex-rs/Cargo.lock

@@ -333,6 +333,54 @@ version = "1.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c08606f8c3cbf4ce6ec8e28fb0014a2c086708fe954eaa885384a6165172e7e8"
 
+[[package]]
+name = "axum"
+version = "0.8.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "021e862c184ae977658b36c4500f7feac3221ca5da43e3f25bd04ab6c79a29b5"
+dependencies = [
+ "axum-core",
+ "bytes",
+ "futures-util",
+ "http",
+ "http-body",
+ "http-body-util",
+ "hyper",
+ "hyper-util",
+ "itoa",
+ "matchit",
+ "memchr",
+ "mime",
+ "percent-encoding",
+ "pin-project-lite",
+ "rustversion",
+ "serde",
+ "sync_wrapper",
+ "tokio",
+ "tower",
+ "tower-layer",
+ "tower-service",
+]
+
+[[package]]
+name = "axum-core"
+version = "0.5.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "68464cd0412f486726fb3373129ef5d2993f90c34bc2bc1c1e9943b2f4fc7ca6"
+dependencies = [
+ "bytes",
+ "futures-core",
+ "http",
+ "http-body",
+ "http-body-util",
+ "mime",
+ "pin-project-lite",
+ "rustversion",
+ "sync_wrapper",
+ "tower-layer",
+ "tower-service",
+]
+
 [[package]]
 name = "backtrace"
 version = "0.3.75"
@@ -956,8 +1004,11 @@ name = "codex-rmcp-client"
 version = "0.0.0"
 dependencies = [
  "anyhow",
+ "axum",
+ "futures",
  "mcp-types",
  "pretty_assertions",
+ "reqwest",
  "rmcp",
  "serde",
  "serde_json",
@@ -2883,6 +2934,12 @@ dependencies = [
  "regex-automata",
 ]
 
+[[package]]
+name = "matchit"
+version = "0.8.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "47e1ffaa40ddd1f3ed91f717a33c8c0ee23fff369e3aa8772b9605cc1d22f4c3"
+
 [[package]]
 name = "mcp-types"
 version = "0.0.0"
@@ -3669,7 +3726,7 @@ dependencies = [
  "once_cell",
  "socket2",
  "tracing",
- "windows-sys 0.52.0",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -3907,20 +3964,29 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "534fd1cd0601e798ac30545ff2b7f4a62c6f14edd4aaed1cc5eb1e85f69f09af"
 dependencies = [
  "base64",
+ "bytes",
  "chrono",
  "futures",
+ "http",
+ "http-body",
+ "http-body-util",
  "paste",
  "pin-project-lite",
  "process-wrap",
+ "rand",
+ "reqwest",
  "rmcp-macros",
  "schemars 1.0.4",
  "serde",
  "serde_json",
+ "sse-stream",
  "thiserror 2.0.16",
  "tokio",
  "tokio-stream",
  "tokio-util",
+ "tower-service",
  "tracing",
+ "uuid",
 ]
 
 [[package]]
@@ -4468,6 +4534,19 @@ dependencies = [
  "windows-sys 0.59.0",
 ]
 
+[[package]]
+name = "sse-stream"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "eb4dc4d33c68ec1f27d386b5610a351922656e1fdf5c05bbaad930cd1519479a"
+dependencies = [
+ "bytes",
+ "futures-util",
+ "http-body",
+ "http-body-util",
+ "pin-project-lite",
+]
+
 [[package]]
 name = "stable_deref_trait"
 version = "1.2.0"