Add a reasoning-off setting (-1 reasoning budget)

Models like DeepSeek V4 Flash reason by default, and the reasoning budget
setting could only ever add thinking tokens - there was no value that turned
thinking off. A negative budget now sends `reasoning: {effort: "none"}`.

Uses effort:none rather than exclude:true deliberately - exclude still thinks
and still bills, it only hides the trace.

Zero keeps its old meaning (send no `reasoning` field at all) so endpoints that
reject unknown fields, like the default Ollama one, are unaffected. Reusing the
existing int column this way avoids a migration.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UeQVy5bEjLhfgWNc27Efet

backend/app/models.py

@@ -307,7 +307,8 @@ class Settings(Base):
     # and left reasoning models with nothing after their thinking.
     max_output_tokens: Mapped[int] = mapped_column(Integer, default=800)
     # Separate thinking budget for reasoning models (OpenRouter-style
-    # `reasoning: {max_tokens}`); 0 = param not sent. Added on top of
+    # `reasoning: {max_tokens}`); 0 = param not sent, -1 = reasoning explicitly
+    # off (`reasoning: {effort: none}`). Added on top of
     # max_output_tokens so story output keeps its full budget.
     reasoning_max_tokens: Mapped[int] = mapped_column(Integer, default=0)
     context_token_budget: Mapped[int] = mapped_column(Integer, default=16384)