[BUG] Agent teams: in-process teammate window header shows the lead's model, not the teammate's actual model

Environment

• Claude Code: 2.1.227 / 2.1.228
• Platform: Linux (Arch, kernel 7.0.10)
• Agent teams: CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1, teammateMode: auto (running outside tmux, so teammates use the in-process backend)
• Lead session model pinned in ~/.claude/settings.json: "model": "claude-fable-5[1m]"
• teammateDefaultModel: "sonnet" set via /config → "Default teammate model"

Bug

When a teammate is spawned (either via the Agent tool with an explicit model, or model-less falling back to teammateDefaultModel) and runs on the in-process backend, the teammate's window/view in the TUI shows the lead session's model ("Fable 5") in the header — not the model the teammate is actually running on.

The teammate genuinely runs the correct model; only the header is wrong.

Repro

1. Enable agent teams, run the lead outside tmux (in-process teammate backend), pin the lead to one model (e.g. Fable/Opus) and set "Default teammate model" to a different one (e.g. Sonnet) in /config.
2. Spawn a teammate via the Agent tool with model: "sonnet" (or omit model so the default applies).
3. Switch to the teammate's window in the TUI and look at the model label at the top.

Expected: header shows the teammate's model (Sonnet 5).
Actual: header shows the lead's model (Fable 5).

Evidence that the teammate really runs the right model

• Team roster ~/.claude/teams/session-*/config.json records the teammate with "model": "sonnet" (and for a model-less spawn, "model": "claude-sonnet-5" resolved from teammateDefaultModel).
• The teammate's transcript (~/.claude/projects/<proj>/<session>/subagents/agent-a<name>-*.jsonl) stamps every assistant message with "model": "claude-sonnet-5".
• Asked to self-report, the teammate answers "I am running as Sonnet 5 (claude-sonnet-5)".

All three disagree with the window header.

Impact

Users conclude that every teammate is burning the expensive lead-tier model and that model routing / teammateDefaultModel is broken, when it is actually working. (That is exactly how this was discovered — an "all my teams spawn as Fable" investigation that turned out to be display-only.) Related-but-different: #68411 reports teammates actually ignoring the configured model; this report is purely the header display for in-process teammates.

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