fix: preserve function responses (#47920)

- adds up to: https://github.com/supabase/cli/pull/5862

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **New Features**
* Added an “Error docs” link in Edge Function testing UI when an
`sb-error-code` header is present.

* **Bug Fixes**
* Improved the Edge Function test proxy to consistently preserve
upstream status, headers (including repeated headers), and response
bodies without transformation.
* Enhanced handling for invalid function URLs and upstream fetch
failures.

* **Tests**
* Added unit, API, and Playwright E2E coverage for error docs linking
and response proxy behavior.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

e2e/studio/features/edge-functions.spec.ts

@@ -0,0 +1,61 @@
+import { expect } from '@playwright/test'
+
+import { test } from '../utils/test.js'
+import { toUrl } from '../utils/to-url.js'
+
+const FUNCTION_SLUG = 'error-code-docs'
+
+test.describe('Edge Functions', () => {
+  test('links an sb-error-code response to its documentation', async ({ page, ref }) => {
+    await page.route(`**/api/v1/projects/${ref}/functions/${FUNCTION_SLUG}`, async (route) => {
+      const timestamp = Date.now()
+      await route.fulfill({
+        contentType: 'application/json',
+        body: JSON.stringify({
+          id: '00000000-0000-0000-0000-000000000000',
+          slug: FUNCTION_SLUG,
+          name: FUNCTION_SLUG,
+          version: 1,
+          status: 'ACTIVE',
+          entrypoint_path: `supabase/functions/${FUNCTION_SLUG}/index.ts`,
+          created_at: timestamp,
+          updated_at: timestamp,
+        }),
+      })
+    })
+    await page.route('**/api/edge-functions/test', async (route) => {
+      await route.fulfill({
+        contentType: 'application/json',
+        body: JSON.stringify({
+          status: 401,
+          headers: { 'sb-error-code': 'UNAUTHORIZED_INVALID_JWT_FORMAT' },
+          body: '',
+        }),
+      })
+    })
+
+    await page.goto(toUrl(`/project/${ref}/functions/${FUNCTION_SLUG}`))
+    await page.getByRole('button', { name: 'Test', exact: true }).click()
+
+    const testResponse = page.waitForResponse(
+      (response) =>
+        response.url().includes('/api/edge-functions/test') &&
+        response.request().method() === 'POST'
+    )
+    await page.getByRole('button', { name: 'Send Request' }).click()
+    expect(
+      (await testResponse).ok(),
+      'Studio proxy should return a successful response envelope'
+    ).toBeTruthy()
+
+    await expect(
+      page.getByRole('link', {
+        name: 'View documentation for UNAUTHORIZED_INVALID_JWT_FORMAT (opens in new tab)',
+      }),
+      'Error response should link to its documentation section'
+    ).toHaveAttribute(
+      'href',
+      'https://supabase.com/docs/guides/functions/error-codes#unauthorizedinvalidjwtformat'
+    )
+  })
+})