Persist chat sidebar width and Living UI visibility

[BharadwajKanneveti]

Summary

This PR persists chat layout preferences so they survive navigation and browser refreshes.

Changes

• Main Chat

  • Persist the task sidebar width in localStorage.
  • Restore the saved width on initial render.
  • Validate stored values by:
    • Falling back to the default width when no value exists.
    • Ignoring invalid (NaN) values.
    • Clamping the restored width between the configured minimum and maximum limits.
  • Save the final sidebar width when resizing ends to avoid unnecessary writes during dragging.

• Living UI

  • Persist the chat panel visibility (Hide Chat / Show Chat) in localStorage.
  • Restore the previous visibility state on initial render so the panel remains hidden or visible across navigation and page refreshes.

Testing

• Main Chat

  • Resized the task sidebar, refreshed the page, and verified the width was restored.
  • Resized the task sidebar, navigated away and back, and verified the width persisted.
  • Verified the default width is used when no saved value exists.

• Living UI

  • Hid the chat panel, refreshed the page, and verified it remained hidden.
  • Hid the chat panel, navigated away and back, and verified it remained hidden.
  • Toggled the chat panel back on and verified the visibility preference persisted.

Closes #379

[BharadwajKanneveti]

Hi @ahmad-ajmal I have made the changes please check and let me know if you find any issue.