refactor(server): drop stale prompt text, duplicated routes and dead options

- lib/system-prompts.ts: delete the extended prompt kept only to reach
  the 4096-token cache threshold of two old Claude models; describe the
  current canvas-first UI in the App Features section
- app/api/chat/route.ts: remove the server-side example cache (the
  browser answers examples itself), the ENABLE_HISTORY_XML_REPLACE
  option and its helper, the unread messageMetadata fields; the
  DEBUG_LLM_PAYLOAD blocks become one describeMessages summary
- app/api/log-feedback and log-save share scoreLatestTrace in
  lib/langfuse.ts
- app/api/admin/test-model and validate-model call a shared
  testModelConnection() instead of one route faking a request to the
  other and passing trust through the body
- lib/dynamo-quota-manager.ts reads the failing item from the
  conditional update instead of a second GetItem
- lib/ai-providers.ts: geminiThinkingOptions helper for the google and
  vertexai cases, drop the unused fourth resolveBaseURL parameter
- edge-functions: always stream, shrink messageSchema, drop model
  aliases nothing sends
- delete app/api/chat/xml_guide.md, parseOutputTokenLimit, unused type
  exports and export keywords on file-internal symbols
- env.example: drop variables nothing reads, document the quota,
  validation and analytics variables, mention the apiKeyEnv array form
  (also in docs/*/ai-providers.md)

tests/unit/admin-providers.test.ts

@@ -48,8 +48,6 @@ describe("deriveEnvUpdates", () => {
         expect(updates.ADMIN_OPENAI_API_KEY).toBe("sk-test")
         expect(updates.OPENAI_API_KEY).toBeUndefined()
         expect(JSON.parse(updates.ADMIN_PROVIDERS as string)).toHaveLength(1)
-        // AI_MODELS_CONFIG is no longer written (merged at read time)
-        expect(updates.AI_MODELS_CONFIG).toBeNull()
     })
 
     it("suffixes env vars for a second instance of the same provider", () => {
@@ -137,7 +135,6 @@ describe("deriveEnvUpdates", () => {
         const prev = [provider()]
         const updates = deriveEnvUpdates([], prev)
         expect(updates.ADMIN_OPENAI_API_KEY).toBeNull()
-        expect(updates.AI_MODELS_CONFIG).toBeNull()
         expect(updates.ADMIN_PROVIDERS).toBeNull()
     })