Show task, active project and workspace per control board row (#1503)

Gate A fix asked by the professor session on Jason's behalf. Each row
now carries three derived fields, shown as "unknown" when the log and
tmux do not hold them:

- task: the session's first user message (pi logs have no task envelope)
- workspace: the live pane path of the pane running pi, else session cwd
- activeProject: basename of the nearest git checkout above the workspace

tmuxInspect replaces the bare liveness call in the CLI and returns
{ alive, workspace }; tmuxIsAlive stays as a wrapper. The grouping column
and seen.json keys are unchanged. Fixture test per field, tmux parse
tests, page test; missing launcher signals are recorded in the plan page.

Co-Authored-By: Claude Fable 5.1 <[email protected]>

BUILD-LOG.md

@@ -2040,3 +2040,26 @@ packages/mosaic 69/69. Live check at 14:27Z on the real board: orch-01
 (assistant + toolCall) working, rev-code-01 (tool result last) working,
 velma (text-only, stop) waiting. Sonnet review: APPROVED, no findings.
 No seat changed state because of this change; it closes a gap, not a bug.
+
+## 2026-09-12 — Control board step 3, Gate A fix: task, project, workspace per row (#1503)
+
+Before: a row said who and what state, but not what the seat was asked to
+do or where it was working. Jason asked (through the professor session)
+for task, project and workspace per row, with "unknown" instead of a guess.
+
+After: readSession records the first user message (task); tmuxInspect
+reads `#{pane_current_command}\t#{pane_current_path}` and returns
+{ alive, workspace }; findRepoRoot walks up from the workspace to the
+nearest `.git` directory or worktree file (activeProject). The grouping
+column and seen.json keys are unchanged. Page: Task and Active project
+columns in all three tables, Task, Active project and Workspace in the
+detail row, every value through esc(), nulls shown as "unknown". Tests:
+six fixture tests (task from blocks, task from a string, no task, workspace
+tmux/cwd/none, activeProject dir/file/none, record on disk) plus parsePanes
+and two tmuxInspect tests and one page test. Suites: control-board 79/79,
+packages/mosaic 69/69. Live check at 14:51Z on a scratch server (port
+7332): 42 rows, all three fields derived on every row, 16 workspaces from
+a live pane, the rest from the log; every fleet seat reads `.mosaic` as
+its active project because `~/.mosaic` is a git checkout and the roster
+names no project. Missing launcher signals are listed in the plan page
+Step 3 log. Sonnet review: APPROVED, no findings.