fix(mcp): eager-auth flag on the Grok connector links so Grok starts OAuth (#2167)

* fix(mcp): eager-auth flag on the Grok connector links so Grok starts OAuth

Live test after #2158: pasting the Grok URL into grok.com's custom
connector dialog listed all 150+ tools and never opened the sign-in. Grok
probes the URL without credentials, like claude.ai, and reads the lazy
200 on initialize as an authless server; only the 401 challenge starts
OAuth (#2159 fixed the same thing for the claude.ai link).

- lib/onboarding/checklist.ts: mcpServerUrl() builds the server URL with
  an optional eagerAuth flag; sideDoorServerUrl() gives the Grok side door
  auth=required and keeps ChatGPT lazy; claudeConnectorLink() reuses it.
  SIDE_DOORS / SideDoor move here from the component. Tests for all three.
- NewUserChecklist copies the door-specific URL (now with a client marker).
- ApiKeysPanel's Grok row copies the flagged URL, mirroring the Claude one.
- auth-mode.ts comment records the second consumer; registry entry's Grok
  step carries the flag; DECISIONS.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LhTJcwgzmN3TsLR8tVHwdi
Signed-off-by: Emil <emilmattsson14@gmail.com>

* docs(mcp): registry Claude.ai step carries auth=required too

Review pass on #2167: the registry entry flagged the Grok install URL
but left the Claude.ai step on the bare URL, which pre-fills "None" in
claude.ai's dialog (#2159). Same file, same flag, now consistent.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LhTJcwgzmN3TsLR8tVHwdi
Signed-off-by: Emil <emilmattsson14@gmail.com>

---------

Signed-off-by: Emil <emilmattsson14@gmail.com>
Co-authored-by: Claude Fable 5.1 <noreply@anthropic.com>

lib/onboarding/__tests__/checklist.test.ts

@@ -2,6 +2,9 @@ import { describe, expect, it } from 'vitest'
 import {
   checklistNumbers,
   claudeConnectorLink,
+  mcpServerUrl,
+  sideDoorServerUrl,
+  SIDE_DOORS,
   claudeStepDone,
   completionPatchBody,
   vatDeadlineLine,
@@ -105,6 +108,39 @@ describe('claudeStepDone', () => {
   })
 })
 
+describe('mcpServerUrl', () => {
+  it('builds the namespaced URL with the client marker and no auth flag by default', () => {
+    expect(mcpServerUrl({ origin: 'https://app.testbrand.example', client: 'cursor' })).toBe(
+      'https://app.testbrand.example/api/extensions/ext/mcp-server/mcp?tool_namespace=accounted&client=cursor',
+    )
+  })
+
+  it('appends auth=required when eagerAuth is set', () => {
+    const url = new URL(mcpServerUrl({ origin: 'http://localhost:3000', client: 'grok', eagerAuth: true }))
+    expect(url.searchParams.get('tool_namespace')).toBe('accounted')
+    expect(url.searchParams.get('client')).toBe('grok')
+    expect(url.searchParams.get('auth')).toBe('required')
+  })
+})
+
+describe('sideDoorServerUrl', () => {
+  it('lists chatgpt then grok', () => {
+    expect(SIDE_DOORS).toEqual(['chatgpt', 'grok'])
+  })
+
+  it('gives Grok the eager-auth flag: its dialog reads a 200 probe as "no auth" and never starts OAuth', () => {
+    const url = new URL(sideDoorServerUrl({ origin: 'https://app.testbrand.example', door: 'grok' }))
+    expect(url.searchParams.get('client')).toBe('grok')
+    expect(url.searchParams.get('auth')).toBe('required')
+  })
+
+  it('keeps ChatGPT on the lazy URL', () => {
+    const url = new URL(sideDoorServerUrl({ origin: 'https://app.testbrand.example', door: 'chatgpt' }))
+    expect(url.searchParams.get('client')).toBe('chatgpt')
+    expect(url.searchParams.get('auth')).toBeNull()
+  })
+})
+
 describe('claudeConnectorLink', () => {
   it('builds the claude.ai deep link with namespace, client marker and eager-auth flag, from the page origin', () => {
     const link = claudeConnectorLink({ origin: 'https://app.testbrand.example', appName: 'Testbrand' })