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