refactor: decompose executeToolsIfNeeded into focused helper methods

Extract 14 helper methods from the monolithic executeToolsIfNeeded method
to improve maintainability and reduce complexity:

- getInitialResponse(): Get initial response from stream or cache
- saveResponseToState(): Save response output to state
- markStateComplete(): Mark conversation complete
- saveToolResultsToState(): Save tool results to state
- checkForInterruption(): Handle interruption signals
- shouldStopExecution(): Evaluate stop conditions
- hasExecutableToolCalls(): Check for executable tools
- executeAutoApproveTools(): Execute non-approval tools
- handleApprovalCheck(): Deduplicated approval workflow
- executeToolRound(): Execute one round of tools
- resolveAsyncFunctionsForTurn(): Resolve async params per turn
- applyNextTurnParams(): Apply nextTurnParams
- makeFollowupRequest(): Build and send follow-up requests
- validateFinalResponse(): Validate final response

The main method is reduced from ~400 lines to ~110 lines, acting as a
clean coordinator that delegates to these focused helpers.

Also replaces 'name as string' casts with String() for safer conversion.

Author: mattapperson