feat(flush): add auto mode with self-injected /clear for unattended runs

Long autonomous sessions bloat or hit auto-compaction because /clear is a prompt keystroke no tool call can execute. Auto mode closes that gap: after the write-verified checkpoint, the agent derives its own tmux pane, arms self-inject.sh through tmux run-shell -b, and ends the turn so /clear and a resume line land at an idle prompt. The server-owned arm is load-bearing: a detached child of a tool call dies at the turn boundary. The pane must be derived before arming because ancestry detection can't work under the tmux server.

self-inject.sh joins the synced scripts with a six-test bats suite, tmux stubbed at the boundary. work-the-backlog now auto-flushes between tasks when context grows heavy, and its speedrun preset gained the per-item disposition rule: feature-level work gets a spec, unguessable decisions get a VERIFY, well-defined tasks get implemented. The mechanism was proven live in another project's session and its design note is preserved under docs/design/.

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