ref(browser): Update browser metrics to avoid deprecations (#10943)

This rewrites browser metrics to:

1. Accept spans instead of transactions
2. Use the new performance APIs instead of the old ones

The only thing I left for now is the tags, which we can get rid of
separately: #10823

Part of #10900

Author: mydea

packages/core/src/tracing/sentrySpan.ts

@@ -371,6 +371,18 @@ export class SentrySpan implements Span {
     Object.keys(attributes).forEach(key => this.setAttribute(key, attributes[key]));
   }
 
+  /**
+   * This should generally not be used,
+   * but we need it for browser tracing where we want to adjust the start time afterwards.
+   * USE THIS WITH CAUTION!
+   *
+   * @hidden
+   * @internal
+   */
+  public updateStartTime(timeInput: SpanTimeInput): void {
+    this._startTime = spanTimeInputToSeconds(timeInput);
+  }
+
   /**
    * @inheritDoc
    */