Group dock and member list show a Bot's work from another room #553

Owner decision (2026-10-20 23:03 Asia/Shanghai): group status rows show only this room's work.

Owner report: "这里不是这个房间的活也显示出来了，紧急修复" (work that does not belong to this room is shown here).

Environment

FlyBot main at ae11e00 (group dock from #548 / #546). Owner's local instance.

Steps to reproduce

1. Have Chief be a member of two groups, e.g. 研发组 and FlyBot 交付组.
2. Let Chief run a tool (a shell command) in FlyBot 交付组.
3. Open 研发组.

Actual

• The dock above 研发组's composer shows Chief · 运行命令: cd /data/dsh/bot/workspace/main && sed -n 55,80p AGENTS.md · 1m.
• 研发组's member list shows the same step under Chief, ending 在 FlyBot 交付组 · 1m.
• The same happens for a Bot busy in its own chat, and for an approval the Bot waits on elsewhere (Chief is waiting for your approval, with the other room's command on the card).

Expected

A group's (or face room's) dock row and its member list's working state show only work in this room: the member's turn in this room, and work handed out from this room (a member here sent it with message_bot, which runs as a hidden turn of the Bot's own chat; see #550/#551). A Bot busy in another room or in its own chat shows nothing here: no row, no "busy elsewhere" line, and none of that room's commands (that room can have different members). The Bot's own chat dock and the sidebar's Bot row still show where it works.

Where it sits

• core/src/client/member-status.js memberWork: doing = local ? … : work.bots?.[id] falls back to the Bot's work anywhere; splitBusy sends it to the SummaryLine; approvals are filtered by Bot only.
• core/src/client/member-status.js MemberWork: prints the step plus in <other room> / in its own chat.
• core/src/host/turns.js workView: an own-chat turn handed out from a group carries no mark of that group, so the client cannot tell it apart from unrelated own-chat work.

Suggested direction

Scope memberWork to this room: the room's own entry, else the Bot's own-chat turn when it was handed out from this room (workView adds fromRoomId, owner-only view). Approvals: this room's, or the handed turn's. Drop the cross-room hint from the dock and the member list.