fix(llm): wire prompt caching through all Anthropic call sites

- page-triage classifier + light-extraction now put the static skill
  prompt in `system:` so the per-document caches hit instead of
  re-sending boilerplate in the user message every call.
- Description generation builders return `{ system, user }` with
  instruction text + word limit moved into the cacheable system.
- Relationship-LLM proposal framing moved to `system:`.
- `KtxMessageBuilder.wrapSimple` skips the history breakpoint for
  single-message calls (cache write that could never be reused).
- Gateway backend now sets `anthropic-beta: extended-cache-ttl-2025-04-11`
  so 1h TTLs don't silently downgrade to 5m on Gateway routes.

packages/llm/src/message-builder.test.ts

@@ -81,6 +81,50 @@ describe('KtxMessageBuilder.build', () => {
     expect((out.tools.z as { providerOptions?: unknown }).providerOptions).toBeUndefined();
   });
 
+  it('wrapSimple does not mark a single user message with a cache breakpoint', () => {
+    const builder = makeBuilder();
+
+    const out = builder.wrapSimple({
+      system: 'SYS',
+      messages: [{ role: 'user', content: 'one-shot prompt' }],
+      tools: {},
+      model: 'anthropic/claude-sonnet-4-6',
+    });
+
+    expect(out.messages).toHaveLength(2);
+    expect(out.messages[0]).toMatchObject({
+      role: 'system',
+      providerOptions: { anthropic: { cacheControl: { type: 'ephemeral', ttl: '1h' } } },
+    });
+    expect(out.messages[1]).toMatchObject({ role: 'user', content: 'one-shot prompt' });
+    expect((out.messages[1] as { providerOptions?: unknown }).providerOptions).toBeUndefined();
+  });
+
+  it('wrapSimple still marks the last history message when there are multiple messages', () => {
+    const builder = makeBuilder();
+
+    const out = builder.wrapSimple({
+      system: 'SYS',
+      messages: [
+        { role: 'user', content: 'turn 1' },
+        { role: 'assistant', content: 'reply 1' },
+        { role: 'user', content: 'turn 2' },
+      ],
+      tools: {},
+      model: 'anthropic/claude-sonnet-4-6',
+    });
+
+    expect(out.messages).toHaveLength(4);
+    expect(out.messages[1]).toMatchObject({ role: 'user' });
+    expect((out.messages[1] as { providerOptions?: unknown }).providerOptions).toBeUndefined();
+    expect(out.messages[2]).toMatchObject({ role: 'assistant' });
+    expect((out.messages[2] as { providerOptions?: unknown }).providerOptions).toBeUndefined();
+    const last = out.messages[3] as { content: Array<{ providerOptions?: unknown }> };
+    expect(last.content[0].providerOptions).toEqual({
+      anthropic: { cacheControl: { type: 'ephemeral', ttl: '5m' } },
+    });
+  });
+
   it('clamps every TTL to 5m for Vertex when vertexFallbackTo5m is enabled', () => {
     const provider = createKtxLlmProvider({
       backend: 'vertex',

packages/llm/src/message-builder.ts

@@ -86,8 +86,13 @@ export class KtxMessageBuilder {
     }
 
     if (input.messages) {
+      // Only mark a history breakpoint when prior turns exist. A single-message call
+      // is the current user turn — marking it writes a cache entry that can't be
+      // reused on the next (different-content) call, costing tokens for nothing.
+      const shouldMarkHistory =
+        cachingActive && this.cacheHistoryEnabled() && input.messages.length > 1;
       messages.push(
-        ...(cachingActive && this.cacheHistoryEnabled()
+        ...(shouldMarkHistory
           ? this.markLastHistoryMessage(input.messages, ttls.historyTtl, input.model)
           : input.messages),
       );

packages/llm/src/model-provider.test.ts

@@ -199,6 +199,9 @@ describe('createKtxLlmProvider', () => {
     expect(createGateway).toHaveBeenCalledWith({
       apiKey: 'gateway-key', // pragma: allowlist secret
       baseURL: 'https://gateway.test/v1',
+      headers: {
+        'anthropic-beta': 'interleaved-thinking-2025-05-14,extended-cache-ttl-2025-04-11',
+      },
     });
     expect(gateway).toHaveBeenCalledWith('anthropic/claude-sonnet-4-6');
   });

packages/llm/src/model-provider.ts

@@ -38,7 +38,7 @@ const DEFAULT_PROMPT_CACHING: KtxPromptCachingConfig = {
   vertexFallbackTo5m: false,
 };
 
-const DIRECT_ANTHROPIC_BETA_HEADER = 'interleaved-thinking-2025-05-14,extended-cache-ttl-2025-04-11';
+const ANTHROPIC_BETA_HEADER = 'interleaved-thinking-2025-05-14,extended-cache-ttl-2025-04-11';
 
 function resolvePromptCaching(config: KtxLlmConfig): KtxPromptCachingConfig {
   return { ...DEFAULT_PROMPT_CACHING, ...config.promptCaching };
@@ -158,7 +158,7 @@ class DefaultKtxLlmProvider implements KtxLlmProvider {
         ...(config.anthropic?.apiKey ? { apiKey: config.anthropic.apiKey } : {}),
         ...(config.anthropic?.baseURL ? { baseURL: config.anthropic.baseURL } : {}),
         headers: {
-          'anthropic-beta': DIRECT_ANTHROPIC_BETA_HEADER,
+          'anthropic-beta': ANTHROPIC_BETA_HEADER,
         },
       });
       return (modelId) => anthropic(modelId);
@@ -178,6 +178,9 @@ class DefaultKtxLlmProvider implements KtxLlmProvider {
     const gateway = (deps.createGateway ?? createGateway)({
       ...(config.gateway?.apiKey ? { apiKey: config.gateway.apiKey } : {}),
       ...(config.gateway?.baseURL ? { baseURL: config.gateway.baseURL } : {}),
+      headers: {
+        'anthropic-beta': ANTHROPIC_BETA_HEADER,
+      },
     });
     return (modelId) => gateway(modelId);
   }