fix(mqtt): emit initial microphone state and drop redundant String() coercion

- speakingIndicator: move #emitMicrophoneState outside the state-change
  guard so the first detected state is published even when it matches
  the initial 'silent' value. Internal #lastEmittedState dedupe still
  prevents redundant IPC traffic.
- mediaStatusService: drop String(state) since state is already a string,
  matching the PR description and updated docblock.

Addresses Gemini review on PR #2497.

Author: IsmaelMartinez

app/browser/tools/speakingIndicator.js

@@ -217,8 +217,8 @@ class SpeakingIndicator {
 						if (this.#overlayVisible) {
 							this.#updateOverlay();
 						}
-						this.#emitMicrophoneState(newState);
 					}
+					this.#emitMicrophoneState(newState);
 				});
 
 				if (foundAudioStats) {

app/mqtt/mediaStatusService.js

@@ -58,7 +58,7 @@ class MQTTMediaStatusService {
 
 	async #handleMicrophoneChanged(event, state) {
 		const topic = `${this.#topicPrefix}/microphone`;
-		await this.#mqttClient.publish(topic, String(state), { retain: true });
+		await this.#mqttClient.publish(topic, state, { retain: true });
 		console.debug('[MQTTMediaStatusService] Microphone state changed to', state, 'published to', topic);
 	}