perf: terminal/IDE badge appears 0.5-1s late — show last-known badge first (SWR)

[grimmerk]

Current behavior

On the Sessions tab, the terminal/IDE badge (ITERM2, VSCODE, …) appears 0.5–1s after the rows themselves. Flow: the list paints immediately (SWR), then detectActiveSessions (process scan) runs in the background, then detectTerminalApps (process-tree walk / AppleScript per PID) fills the badges — only active sessions get one, and only after both async steps resolve.

Proposal: show the last-known badge first (SWR, same pattern as active dots)

• Keep the last successful sessionId → terminalApp map (in-memory across window shows; optionally persisted so the first show after app start also benefits).
• Render the cached badge immediately for sessions that are active per the cached active map; replace/remove it when fresh detection resolves.
• Risk is minor: a stale badge for a session that moved to a different terminal between shows (rare; corrected within ~1s by the fresh pass).

Notes

• Reported during Batch 1 testing (PR feat(sessions): Batch 1 — full-prompt search, match snippets, junk fold, highlight fix #132) — behavior exists in both old and new builds; not a regression.
• Related: perf: session tab switching performance regression (PR #103) #106 (session tab perf), docs/session-finding-plan.md.

🤖 On behalf of @grimmerk — generated with Claude Code