feat: add start field to task panel

[Hell1213]

Added start date field support to task creation, allowing users to set when a task begins.

• Backend: Added start field to AddTaskRequestBody model and AddTaskToTaskwarrior function

• Frontend: Added start date input field in task creation dialog

• Contributes to Add more Fields to the Add Task Panel #188

Checklist

• Ran npx prettier --write . (for formatting)
• Ran gofmt -w . (for Go backend)
• Ran npm test (for JS/TS testing)
• Added unit tests, if applicable
• Verified all tests pass
• Updated documentation, if needed

Additional Notes

The start field follows the same pattern as other optional date fields (due, wait, entry). Empty strings are used to indicate when no start date is set, consistent with existing codebase conventions.

Demo:

Screencast.from.2025-12-19.17-05-17.mp4

[github-actions]

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[Hell1213]

added DatePicker component for start date field in task creation

[Hell1213]

Added start parameter to addTaskToBackend function and conditional logic to include in request body

[Hell1213]

Replaced empty string with actual start date "2025-03-01"

[Hell1213]

Completed self-review . Backend and frontend properly handle optional start field. Tests passing. Ready for review.

[Hell1213]

Hey @its-me-abhishek,
FYI before testing this PR, please set in date-picker.tsx.
This should allow PR #283 to be tested smoothly.

[its-me-abhishek]

Please checkout for conflicts introduced by the recent merge

[Hell1213]

Please checkout for conflicts introduced by the recent merge

thanks, will resolve all conflicts and push shortly