[FEATURE]: Show current variant in TUI status bar #38015

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

Description
When cycling through model variants with ctrl+t (variant_cycle), there is no visual indication in the TUI of which variant is currently active. This makes it hard to know whether you're on high, low, max, etc. without remembering the number of times you pressed the keybind.
Proposed solution
Display the active variant name in the TUI status bar, next to the model name or mode indicator (bottom-right area where build/plan is shown). For example:
claude-sonnet-4-5 | build | high
Or as a badge/chip next to the model name.
Alternatives considered

• Binding variant_list to a key — shows the list but doesn't persist the current selection visibly.
• /details — shows tool execution info but not the active variant.
• /thinking — only toggles thinking block visibility, not the variant.
  Additional context
• Related keybind: variant_cycle (ctrl+t)
• Related keybind: variant_list (defaults to none)
• The agent mode (build/plan) already has a visible indicator; variant should follow the same pattern.