[BUG] Thinking throbber gets stuck in infinite refresh loop

Description

The thinking throbber/spinner gets stuck in an infinite loop, continuously refreshing without making progress. This appears to be a UI rendering issue where the status indicator keeps updating indefinitely.

Environment

• Platforms affected: Both macOS and WSL/Linux
• macOS version: Darwin 25.0.0 (M1 Pro MacBook Pro)
• WSL/Linux: Also reproduces on WSL

Expected Behavior

The thinking throbber should display while Claude is processing, then stop when the response is ready or an error occurs.

Actual Behavior

The thinking throbber enters an infinite loop, continuously refreshing/redrawing. The UI appears stuck and doesn't recover without intervention.

Reproduction

The issue occurs spontaneously during normal Claude Code usage. The exact trigger is unclear, but it happens consistently enough to be noticeable across multiple platforms.

Impact

• Blocks normal usage of Claude Code
• Requires restarting the session
• Affects user experience across multiple platforms (not platform-specific)

Possibly Related Issues

• #769 - Screen flickering during thinking (closed, but may share root cause)
• #759 - Claude hanging during thinking (closed, but similar symptoms)

Additional Context

This appears to be a terminal UI rendering issue specifically related to the status indicator refresh logic.