✨ feat: Add streaming support (#125)

This adds:
- [x] Keyboard and mouse handling on the frontend
- [x] Video and audio streaming from the backend to the frontend
- [x] Input server that works with Websockets

Update - 17/11
- [ ] Master docker container to run this
- [ ] Steam runtime
- [ ] Entrypoint.sh

---------

Co-authored-by: Kristian Ollikainen <14197772+DatCaptainHorse@users.noreply.github.com>
Co-authored-by: Kristian Ollikainen <DatCaptainHorse@users.noreply.github.com>

packages/input/src/latency.ts

@@ -0,0 +1,54 @@
+type TimestampEntry = {
+  stage: string;
+  time: Date;
+};
+
+export class LatencyTracker {
+  sequence_id: string;
+  timestamps: TimestampEntry[];
+  metadata?: Record<string, any>;
+
+  constructor(sequence_id: string, timestamps: TimestampEntry[] = [], metadata: Record<string, any> = {}) {
+    this.sequence_id = sequence_id;
+    this.timestamps = timestamps;
+    this.metadata = metadata;
+  }
+
+  addTimestamp(stage: string): void {
+    const timestamp: TimestampEntry = {
+      stage,
+      time: new Date(),
+    };
+    this.timestamps.push(timestamp);
+  }
+
+  // Calculates the total time between the first and last recorded timestamps.
+  getTotalLatency(): number {
+    if (this.timestamps.length < 2) return 0;
+
+    const times = this.timestamps.map((entry) => entry.time.getTime());
+    const minTime = Math.min(...times);
+    const maxTime = Math.max(...times);
+    return maxTime - minTime;
+  }
+
+  toJSON(): Record<string, any> {
+    return {
+      sequence_id: this.sequence_id,
+      timestamps: this.timestamps.map((entry) => ({
+        stage: entry.stage,
+        // Fill nanoseconds with zeros to match the expected format
+        time: entry.time.toISOString().replace(/\.(\d+)Z$/, ".$1000000Z"),
+      })),
+      metadata: this.metadata,
+    };
+  }
+
+  static fromJSON(json: any): LatencyTracker {
+    const timestamps: TimestampEntry[] = json.timestamps.map((ts: any) => ({
+      stage: ts.stage,
+      time: new Date(ts.time),
+    }));
+    return new LatencyTracker(json.sequence_id, timestamps, json.metadata);
+  }
+}