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)

lib/admin/providers.ts

@@ -56,7 +56,7 @@ const StoredAdminProviderSchema = AdminProviderSchema.extend({
     vertexApiKey: z.string().optional(),
 })
 
-export type AdminProviderInput = z.infer<typeof AdminProviderSchema>
+type AdminProviderInput = z.infer<typeof AdminProviderSchema>
 
 // Stored form: secrets are plain strings
 export interface StoredAdminProvider {
@@ -115,7 +115,7 @@ export function loadAdminProviders(): StoredAdminProvider[] {
     }
 }
 
-export type MaskedAdminProvider = Omit<
+type MaskedAdminProvider = Omit<
     StoredAdminProvider,
     (typeof SECRET_FIELDS)[number]
 > & {
@@ -278,15 +278,9 @@ export function deriveEnvUpdates(
     return updates
 }
 
-// Every settings key the panel may have written for a given list.
-// AI_MODELS_CONFIG is included to clean up values written by older
-// versions of the panel (it is no longer written).
+// Every settings key the panel may have written for a given list
 function derivedEnvKeys(list: StoredAdminProvider[]): string[] {
-    const keys = new Set<string>([
-        "AI_MODELS_CONFIG",
-        "AI_PROVIDER",
-        "AI_MODEL",
-    ])
+    const keys = new Set<string>(["AI_PROVIDER", "AI_MODEL"])
     const indexByProvider = new Map<ProviderName, number>()
     for (const p of list) {
         const index = indexByProvider.get(p.provider) ?? 0