teams: one wake per reply, stops reach background members, the belt follows the role, and four store fixes

[AbirAbbas]

Follows #1429 / #1485 / #1494 / #1436 review: the seven team manager and store should-fixes. One commit per item.

What was wrong → what is true now

1. A member's reply woke its manager, and the finished of the same member turn, ~13 s later, woke it again. That doubled the paid turns, and the 10-wake loop breaker tripped after ~5 real rounds. → One reply is one wake. The dedupe is read back from the Traffic, so it holds across a restart. The ending reaches the manager at its next step. A finished with no reply, a failure or a question still wakes it, and ten wakes are now ten replies.
2. Teams.Name / Teams.Propose with a zero or negative Budget gave the engine's model call no deadline. → Zero uses the engine's 30 s ceiling, and every budget is capped at it. A negative budget answers deadline exceeded without a call.
3. A demoted manager kept every team verb, each refusing. → The belt matches the role at the next step, and the other tools keep their order. A remembered call is told team_send is no longer one of your tools: this conversation no longer manages a team. An unreadable teams file removes nothing.
4. team_stop could not stop a member codeaf opened in the background, because only a window performed the stop. → The member's own session honours its manager's stop while a turn runs (the manager stopped this turn). It ignores old stops, stops for others and stops from links, and never touches a turn that has already ended. The tool reply and the manual say it stops again.
5. Closing a sub-team whose manager alone was working closed it at once while the manager kept running. → The card opens with Wrap up first leading and names the manager. Close now stops that manager's turn but keeps its tab, because it is still in the team above.
6. An unreadable day spend counted as $0, so a team's cap stopped holding. → Fail closed: harbor has a $5 daily cap and today's spend could not be read (<error>), so nothing new starts until it can be read. No cap card is raised, the next check retries, and an uncapped team never reads the spend.
7. Packet rotation dropped answered packets after two rotations: an answer its asker had not run to see yet, and today's cap decision. → The asker's delivery appends a told line. Rotation now carries waiting packets, today's cap packets, and answers not yet told, newest first within half the rotation size.

Every change updates the manual (team-manager.md, team-questions-and-caps.md, teams-page.md), with retrieval probes and dated notes in DESIGN.md.

Validation contract, and how it was checked
Each item has a test derived from the contract, and each fails on origin/dev by construction. On dev the manager is woken a second time, the zero budget has no deadline, team_send stays on the belt, the headless member's turn never ends, the close happens at once, the hold is empty, and the rotated packet is ErrNoPacket. They pass here:

• TestTeamWake{AReplyAndItsFinishedTurnWakeTheManagerOnce,FinishedAfterReplyStillDeduplesAfterManagerRestart,TheLoopBreakerCountsTenMemberReplies}
• TestTeamAskBudgetBoundsEveryModelCall, TestExpiredTeamAskNeverCallsTheModel
• TestTeamRoleDemotionRemovesOnlyLostVerbsAndRearmingAppends, TestTeamToolsLeaveWhenTheTeamsFileIsGone
• TestTeamStop{EndsAHeadlessMembersCurrentTurn,IgnoresOldOtherAndSharedStops}
• TestTeamsCloseCountsAndStopsASubteamManagerSharedWithItsParent
• TestTeamUnreadableSpendHoldsCappedWorkWithoutAPacket, TestTeamCapHoldsWhenTheUsageLedgerPathIsADirectory, TestTeamWithoutACapNeverReadsAnUnreadableLedger
• TestRotationKeepsAnUntoldAnswerAcrossSeveralFiles, TestTodaysCapDecisionSurvivesRotationAndOwedCarryStaysBounded, TestTeamAnswerDeliveredAfterPacketRotationsIsMarkedTold

The whole TestTeam* session group passes, along with the teams, remote and manual packages, the tui3 close tests and make pr-ready.

The loop-breaker test failed once inside a long package run. It used a positional script, and another request of the member's took the next round's step. Its rounds are now armed per request, and it passes alone and in the same full group run where it had failed.

There was no real-binary hand check: every changed behaviour is in the engine, the store, or the close card's model, and the tests above drive each one directly.

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