feat: introduced external thinking support and private scratchpad think tool

- Added support for external thinking and forced reasoning disablement across AI provider options and request transformers.
- Implemented the private scratchpad think tool along with its renderer, system prompt rules, and schema configuration.
- Updated agent session management and SDK tools to support dynamic runtime activation of the think tool via the externalThinking setting.
- Added comprehensive unit tests covering reasoning fallbacks, tool activation, and rendering behavior.

packages/coding-agent/src/modes/controllers/selector-controller.ts

@@ -479,6 +479,11 @@ export class SelectorController {
 					this.ctx.showError(`Failed to apply vision mode: ${err}`);
 				});
 				break;
+			case "externalThinking":
+				void this.ctx.session.setThinkToolEnabled(value as boolean).catch(err => {
+					this.ctx.showError(`Failed to apply external thinking: ${err}`);
+				});
+				break;
 
 			case "autocompleteMaxVisible":
 				this.ctx.editor.setAutocompleteMaxVisible(typeof value === "number" ? value : Number(value));