fix(voice): send greeting trigger in reactive mode for Gemini

Gemini Live has no built-in first-message like ElevenLabs agents do;
without an explicit turnComplete:true it sits silently. In reactive mode
(default, toggle off) now sends a greeting instruction after any silent
context feed so Gemini introduces itself and invites the user to speak.

Proactive mode is unchanged: the context summary is the opening speech.

via [HAPI](https://hapi.run)

Co-Authored-By: HAPI <noreply@hapi.run>

Author: heavygee

web/src/realtime/GeminiLiveVoiceSession.tsx

@@ -181,13 +181,18 @@ class GeminiLiveVoiceSessionImpl implements VoiceSession {
                     // Start audio capture
                     startAudioCapture(state.playbackContext!)
 
-                    // Send initial context if available (no clientContent greeting — it breaks tool calls)
-                    // In reactive mode (default) send silently so Gemini doesn't narrate on connect.
+                    const proactive = localStorage.getItem('hapi-voice-proactive') === 'true'
+
                     if (config.initialContext) {
-                        const proactive = localStorage.getItem('hapi-voice-proactive') === 'true'
+                        // Proactive: speak the summary. Reactive: feed context silently.
                         sendClientContent(`[Context] ${config.initialContext}`, proactive)
                     }
 
+                    if (!proactive) {
+                        // Gemini won't self-start; send a greeting trigger so it introduces itself.
+                        sendClientContent('[Introduce yourself briefly and invite the user to speak.]', true)
+                    }
+
                     resolve()
                     return
                 }