feat(coding-agent): surfaced lazy LSP servers as available in welcome screen

- Added "available" status so recognized servers show under lazy mode without warmup.
- Rendered full welcome box as pre-TUI splash with fixed slot heights to avoid layout shift.
- Reported lazy servers as available in /status instead of omitting the section.

packages/coding-agent/src/session/session-manager.ts

@@ -1516,10 +1516,10 @@ class NdjsonFileWriter {
 	}
 }
 
-/** Get recent sessions for display in welcome screen */
+/** Get recent sessions for display in welcome screen (which reserves WELCOME_SESSION_SLOTS rows) */
 export async function getRecentSessions(
 	sessionDir: string,
-	limit = 3,
+	limit = 4,
 	storage: SessionStorage = new FileSessionStorage(),
 ): Promise<RecentSessionInfo[]> {
 	const sessions = await getSortedSessions(sessionDir, storage);