docs(integration-branch): sync the skill with the tb-streamer copy

[RonenMars]

Brings this copy up to the state the tb-streamer copy reached today, in both .claude/ and .agents/ (kept byte-identical).

Imported from tb-streamer

• Flow B removed — the only path that writes to origin now replays a rehearsal.
• Flow C's output renamed the execution log and execution summary, each opening with a pointer to the rehearsal pair it replays.
• Per-PR checkbox gate, with a Backed by table for boxes only a human can tick (on-device / manual steps get disclosed before they are ticked, never ticked quietly).
• Rebase-recovery ladder built on git cherry's patch-id comparison, which survives a rebased base where every SHA changed.
• Section for a PR whose head branch was cut from the integration branch — the one written for this repo after fix(servers): show a friendly error when cache-alert resolve fails #784/refactor(ui): share alert spec between toasts and banners #785 and never landed here until now.
• A fix this run writes goes on a branch cut from main, with dependency notes using bare PR numbers so GitHub's closing keywords cannot fire.
• Dependabot question at the start of flow A and its carry-forward into flow C; Step 2 abort recipe; Step 9 cleanup; stale-worktree prune.
• The explicit --force-with-lease=<branch>:<old-head> everywhere the skill force-pushes.

Kept from this repo

Everything this repo had and tb-streamer did not:

• the branch-expiry policy and its retirement doc
• ### Retire the branch and ### Coordinating with tb-streamer
• the traps rows for test:unit as a false green, Maestro never running on a PR, hand-writing [skip-ci], and committing a fix to the integration branch

Streamer's commands are replaced by this repo's five required checks (lint, typecheck, test:unit, test:integration, test:i18n), and its native-module note by check:native-deps.

One contradiction resolved in this repo's favour

The imported cleanup table kept the integration branch; this repo retires it once main holds its content.
That row now points at "Retire the branch".

Documentation only.