Two coupled defects made a parked-then-resumed approval turn rehydrate wrong
on a cold reload:

- The runner re-persisted the user prompt on every resume. An approval reply's
  tail is the tool_result envelope (no text), so resolvePromptText fell back to
  the ORIGINAL prompt and wrote a duplicate user row. Guard the write with
  tailIsFreshUserMessage so the prompt persists only on the turn that introduced
  it.
- Nothing marked a turn that ended mid-approval. finish() now stamps
  stopReason:"paused" on the terminal `done` record (existing wire field, no
  contract change); transcriptToMessages carries it to message.metadata.paused.

With the duplicate row gone, AgentConversation's server-transcript adoption can
no longer lean on a bumped message count. Make it state-aware: adopt when the
server is ahead by count OR when the local tail is stuck paused while the server
turn is terminal (a resume that completed elsewhere).

Adds paused-end-marker coverage to transcriptToMessages.test.ts.

On cold replay `messageTranscript` fed both pause-terminalization sentinels to the
model through the generic `[<tool> error: …]` branch. The "error" framing makes the
model read a parked call as a refusal and abandon it (the parallel-approval bug), and
for an approved-but-unobserved call it invites a retry of something that may already
have run.

Render each sentinel as an explicit, non-error nudge with opposite guidance:
- DEFERRED_NOT_EXECUTED — skipped for another approval, not denied; re-issue the call.
- APPROVED_EXECUTION_RESULT_UNKNOWN — may already have run; do not assume failure, do
  not retry a side-effecting call.

The user-facing render already distinguishes both (ToolActivity); this restores the
model-facing half dropped when the fix train folded the deferred check into the
combined isPauseSyntheticResult.

…local tail

The paused-tail adoption exception could fire when the server transcript was
shorter than the local one: a lagging snapshot ending in a settled assistant
message would discard newer locally persisted approval state. The intended case
(a resume that completed elsewhere) always has the server at least as long, so
require serverMsgs.length >= prev.length and an assistant tail for the exception.