[FEATURE] Add option to fully disable Sprocket (spinner mascot) in UI

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

There is currently no way to fully disable the Sprocket ASCII cat that appears during processing. The existing settings (reduceMotion: true, spinnerTipsEnabled: false, CLAUDE_CODE_SIMPLE: "1") do not remove the mascot — it still renders in the UI.
This is a significant UX issue for many users. During active coding sessions, the animated character draws attention away from the actual work. It appears right in the middle of the interface, takes up vertical space, and is visually distracting — especially during long-running tasks where it stays on screen for extended periods.

Proposed Solution

A setting like "showMascot": false or "sprocketEnabled": false in ~/.claude/settings.json that completely hides the mascot and replaces it with a simple text-based spinner or nothing at all.
Current workarounds
None of the following work:

"reduceMotion": true
"spinnerTipsEnabled": false
"env": { "CLAUDE_CODE_SIMPLE": "1" }

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_