feat: publish Coder MCP server to official MCP Registry (#21673)

## Summary

This adds the necessary configuration to publish Coder's remote MCP
server to the official MCP Registry at registry.modelcontextprotocol.io.

## Changes

- **`server.json`**: MCP server metadata for registry discovery
- **`.github/workflows/publish-mcp-registry.yaml`**: GitHub Actions
workflow to automatically publish on release

## How it works

1. When a new Coder release is published, the workflow automatically
publishes to the MCP Registry
2. MCP clients (Claude, ChatGPT, VS Code, etc.) can discover Coder via
the registry
3. Users just need to provide their Coder deployment URL - OAuth handles
authentication automatically via RFC 7591 Dynamic Client Registration

## MCP Registry Entry

The server will be listed as `io.github.coder/coder` with:
- **Transport**: `streamable-http` 
- **Endpoint**: `{coder_url}/api/experimental/mcp/http`
- **Auth**: OAuth2 (automatic via
`/.well-known/oauth-authorization-server`)

## Testing

After merge and next release, verify at:
```bash
curl "https://registry.modelcontextprotocol.io/v0.1/servers?q=io.github.coder"
```

Closes #21275

---
_Generated with `mux` • Model: `anthropic:claude-opus-4-5` • Thinking:
`medium`_

---------

Co-authored-by: Ben Potter <me@bpmct.net>

.github/workflows/publish-mcp-registry.yaml

@@ -0,0 +1,80 @@
+name: Publish to MCP Registry
+
+on:
+  release:
+    types: [published]
+  workflow_dispatch:
+    inputs:
+      version:
+        description: "Version to publish (semver, e.g. 2.20.0). Used only for manual runs."
+        required: false
+        type: string
+      publish:
+        description: "Actually publish to the live registry. Leave false to validate only."
+        required: false
+        default: false
+        type: boolean
+
+jobs:
+  publish-mcp:
+    runs-on: ubuntu-latest
+    permissions:
+      id-token: write # Required for GitHub OIDC
+      contents: read
+
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+        with:
+          persist-credentials: false
+
+      - name: Install mcp-publisher
+        run: |
+          curl -L "https://github.com/modelcontextprotocol/registry/releases/latest/download/mcp-publisher_$(uname -s | tr '[:upper:]' '[:lower:]')_$(uname -m | sed 's/x86_64/amd64/;s/aarch64/arm64/').tar.gz" | tar xz mcp-publisher
+
+      - name: Determine version
+        id: version
+        env:
+          EVENT_NAME: ${{ github.event_name }}
+          INPUT_VERSION: ${{ inputs.version }}
+        run: |
+          set -euo pipefail
+          if [ "${EVENT_NAME}" = "release" ]; then
+            # Tag refs look like refs/tags/v2.20.0
+            VERSION="${GITHUB_REF#refs/tags/v}"
+          else
+            VERSION="${INPUT_VERSION}"
+          fi
+
+          if [ -z "${VERSION}" ]; then
+            echo "::error::No version provided. Pass the 'version' input for manual runs."
+            exit 1
+          fi
+
+          # Reject anything that isn't clean semver so we never publish refs/heads/... etc.
+          if ! echo "${VERSION}" | grep -Eq '^[0-9]+\.[0-9]+\.[0-9]+(-[0-9A-Za-z.-]+)?$'; then
+            echo "::error::Refusing to publish invalid version '${VERSION}'."
+            exit 1
+          fi
+
+          echo "version=${VERSION}" >> "${GITHUB_OUTPUT}"
+
+      - name: Set version in server.json
+        env:
+          VERSION: ${{ steps.version.outputs.version }}
+        run: |
+          set -euo pipefail
+          jq --arg v "${VERSION}" '.version = $v' server.json > server.tmp
+          mv server.tmp server.json
+          cat server.json
+
+      - name: Validate server.json (no publish)
+        run: ./mcp-publisher validate
+
+      - name: Authenticate to MCP Registry
+        if: github.event_name == 'release' || inputs.publish
+        run: ./mcp-publisher login github-oidc
+
+      - name: Publish server to MCP Registry
+        if: github.event_name == 'release' || inputs.publish
+        run: ./mcp-publisher publish