Reproduction steps:
1. Open any other project and keep it open while testing
2. Open the attached “WebGL_ProfilerTest.zip” project
3. Go to the Build Profiles settings
4. Make sure the WebGL Platform is selected
5. Make sure Development Build and Autoconnect Profiler are enabled
6. Build and Run the project for WebGL
7. When the project is built observe the Profiler Window that opens in the Editor

Expected result: The built Player is connected to the Profiler and is receiving data
Actual result: The Profiler is not receiving any data. The project opened in the 1st step, has "Profiler connected to Autoconnected Player…" Console log and manually opening Profiler in that project shows that the data is received in the wrong Unity Editor project

Reproducible with: 2022.3.57f1, 6000.0.35f1, 6000.1.0b3, 6000.2.0a1

Reproducible on: Windows 11
Not reproducible on: No other environment tested

Notes:
- Appears to only reproduce if the other project is opened first (the one in the 1st step) and only then opening the WebGL project
- In the 2021.3 version the Scene would not even load when performing the repro steps and would only start showing the Scene after the 1st open project was closed
- Does not reproduce when building for Windows Platform