feat(api): add HTTP and WebSocket APIs (API Gateway v2) to the API Gateway page

API Gateway v2 is a separate AWS API from REST APIs, so HTTP and WebSocket APIs
made with the SDK, SAM, CDK or Terraform never showed up. The API Gateway page
now lists all three kinds with a Type column, creates each from the same form,
and opens HTTP and WebSocket APIs in their own panel:

- Quick create: an HTTP API with a Lambda gets a catch-all route on an
  auto-deployed $default stage, plus the Lambda permission.
- Routes to Lambda (payload 2.0) or HTTP backends; deleting a route removes
  the integration and Lambda permission only it used.
- Stages with or without automatic deployment, and deploy on demand.
- JWT authorizers filled in from a Cognito pool's OpenID Connect discovery
  document and an app client, or from any issuer; protect routes with them.
- CORS configuration.
- A tester that sends a real request to a stage, and for WebSocket APIs one
  that connects, sends a message and collects the replies.

Capabilities are advertised under a new httpApiActions group, covered by the
cloudProxy guard test. Verified end to end against TheCloud's runtime.

packages/frontend/src/components/ApiGatewayRoutePanel.tsx

@@ -8,6 +8,7 @@ import type {CloudResource} from '@/types/resource'
 import {CopyValueButton} from './CopyValueButton'
 import {LogsQueryPanel} from './LogsQueryPanel'
 import {ServiceIcon} from '@/components/serviceIcons'
+import {formatResponseBody, invokeEndpoint, parseHeaders} from '@/lib/apiGateway'
 
 interface ApiGatewayRoutePanelProps {
     cloud: CloudProvider
@@ -138,8 +139,8 @@ export function ApiGatewayRoutePanel({cloud, resource, runtimeReachable, runtime
         return (
             <section className="table-panel">
                 <div className="empty compact">
-                    <h3>Select a REST API</h3>
-                    <p>Select an API Gateway REST API to connect a route to a Lambda function.</p>
+                    <h3>Select an API</h3>
+                    <p>Select an API to see its routes, or create one.</p>
                 </div>
         </section>
         )
@@ -513,49 +514,6 @@ function MethodTestResponse({result, dismiss}: {result?: ApiGatewayMethodTestRes
     </div>
 }
 
-function invokeEndpoint(runtimeEndpoint?: string): string | null {
-    if (!runtimeEndpoint) return null
-    try {
-        const endpoint = new URL(runtimeEndpoint)
-        if (isDockerBridgeAddress(endpoint.hostname) && typeof window !== 'undefined') {
-            endpoint.hostname = window.location.hostname
-        }
-        return endpoint.toString().replace(/\/$/, '')
-    } catch {
-        return runtimeEndpoint.replace(/\/$/, '')
-    }
-}
-
-function isDockerBridgeAddress(hostname: string): boolean {
-    const octets = hostname.split('.').map(Number)
-    return octets.length === 4
-        && octets.every((octet) => Number.isInteger(octet) && octet >= 0 && octet <= 255)
-        && octets[0] === 172
-        && octets[1] >= 16
-        && octets[1] <= 31
-}
-
-function parseHeaders(value: string): Record<string, string> {
-    let parsed: unknown
-    try {
-        parsed = JSON.parse(value || '{}')
-    } catch {
-        throw new Error('Request headers must be valid JSON.')
-    }
-    if (!parsed || typeof parsed !== 'object' || Array.isArray(parsed) || Object.values(parsed).some((header) => typeof header !== 'string')) {
-        throw new Error('Request headers must be a JSON object with string values.')
-    }
-    return parsed as Record<string, string>
-}
-
-function formatResponseBody(body: string): string {
-    try {
-        return JSON.stringify(JSON.parse(body), null, 2)
-    } catch {
-        return body || '(empty response body)'
-    }
-}
-
 function buildCurlCommand(apiId: string, stage: string, path: string, method: string, headersText: string, query: string, body: string): string {
     let headers: Record<string, string> = {}
     try {