Document the claim: a "Claiming a card" section and the Assignee field

AGENTS.md gains the convention — claiming is moving, the assignee is who
launches agents on the card, hand-moves bypass the claim and should update
the line by hand, and git identities collide the way git's do — plus the
**Assignee:** header field beside Status/Priority/Type and the
BOARD_COMMIT_MOVES gate with its unpushed-main consequence.
.env.example documents the setting with its default (off).

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

manager/core/.env.example

@@ -57,6 +57,16 @@ BOARD_PR_POLL_INTERVAL=60
 # means today's behaviour, never a blocked launch.
 BOARD_FETCH_TIMEOUT=10
 
+# Claim on move, and commit it. On: a board-made move out of backlog/ or
+# to-do/ writes **Assignee:** <git user.name> into the task file (first
+# claim only — an existing assignee is preserved), walking a card back to
+# backlog/ clears it, and each move commits itself — the move and the claim
+# in one commit touching only that task file, messaged
+# `board: <number> → <stage> (<name>)`. Nothing is pushed. Off (the
+# default) means today's behaviour exactly: no assignee, no commit, tasks/
+# committed by hand. Anything but empty/0/false/no/off turns it on.
+BOARD_COMMIT_MOVES=
+
 # Seconds between disk polls of the stage directories.
 BOARD_WATCH_INTERVAL=2