inspect: show the final judge phase in the TUI

Keep the dashboard alive after inspectors finish when profile-native auto synthesis is enabled. The judge now runs while the TUI shows a final phase row (for example 'judge: claude-code' with a judging spinner), then the TUI exits automatically and flushes the buffered dump/verdict output.

TTY auto-synthesis now buffers post-run stdout (DumpSink + SynthesisSink) while the alt-screen is active and flushes it after PostRunComplete, so the judge can update the TUI without corrupting terminal output. Legacy prompted synthesis still exits the TUI before prompting.

Also clarifies the Sink contract: AgentEvent must not block, but serialized RunFinished post-run work is allowed.