refactor(ai-client): unify OpenAI-compatible path to AI SDK generateText

Eliminate the dual code path (raw fetch vs AI SDK) for text and vision.
All providers now go through createLanguageModel() + generateText(),
removing chatOpenAiCompatible/analyzeOpenAiCompatible, the manual Usage
type, summarizeUsage, and responseFormat plumbing from 8 call sites.

Key fix: @ai-sdk/openai v3 defaults to the Responses API (/responses);
DeepSeek only supports Chat Completions, so we use .chat() explicitly.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

lib/engine/agents/writer.ts

@@ -423,7 +423,7 @@ export async function runWriterPlan(
       { role: "system", content: WRITER_PLAN_SYSTEM },
       { role: "user", content: buildWriterPlanUserMessage(session) },
     ],
-    { temperature: 0.9, responseFormat: "json_object", tag: "writer-plan" },
+    { temperature: 0.9, tag: "writer-plan" },
   );
 
   const parsed = parseJsonLoose<RawPlan>(raw);
@@ -473,7 +473,7 @@ export async function runWriterBeats(
       { role: "system", content: WRITER_BEATS_SYSTEM },
       { role: "user", content: buildWriterBeatsUserMessage(session, plan) },
     ],
-    { temperature: 0.9, responseFormat: "json_object", tag: "writer-beats" },
+    { temperature: 0.9, tag: "writer-beats" },
   );
 
   const parsed = parseJsonLoose<RawBeats>(raw);