[martiGIT]

Closes #511

Summary

Pane Search (Alt+K) now also lists agent panes from the other ready servers, reusing the connections.agent_sessions summaries behind the All servers sidebar (#494). The summaries load only while search mode is open.

• Active-server panes keep their order and come first. Other servers' agents follow, attention first (sortAgentPanes(..., "attention")).
• Once another server has agents, every row shows a server badge. The server label is part of the search text.
• Remote entries carry their source and open through openServerSession. Local entries still use store.focusPane.
• Pane IDs are only unique per server, so list keys and option IDs use paneJumpEntryKey (connection ID + pane ID for remote entries).
• The search field moves into an inset, rounded wrapper with a lucide Search icon and inherits the base input focus style. Before, the edge-to-edge field drew the global focus ring as stray lines.
• FEATURES.md "Pane Search" describes the cross-server results.

Recent switching (panes.recent) is unchanged and still covers only the active server.

Verification

• bun test web/src/paneJump.test.ts: 13 pass. New cases: active-server skip, server and tab term matching, unique keys across servers.
• format, lint (one existing TerminalView warning) and typecheck pass. bun run build:linux-x64: initial JS 802.0/805 KiB, gzip 247.3/256 KiB, CSS 181.4/196 KiB.
• test:quick in oven/bun:1.4.4 with git and ssh installed: 3921 pass, 5 skip, 13 fail. All failures are in server tests this PR does not touch (SSH shell file mutations, Codex transcript lookup, update installation). The Codex and update-install failures also reproduce on unmodified main in the same container.
• Manual check in a desktop browser against a Local Herdr plus SSH profiles with agents: results from every server appear with badges, multi-term search across server and tab works, and Enter or click opens the agent on its own server.

Compatibility

Frontend only. No protocol, config or API changes.