You've done a great job troubleshooting!
34% usage by engine seems quite high.. It's possible that the issue is not with your project. Have you checked CPU usage in other projects? For example, try the Kiwi Story game - is the performance much better there? For reference, on my pretty old laptop I'm getting about 25% total CPU utilization, 10% draw calls and only 2% engine.
If the numbers are much higher on your machine, try different browsers - Edge, Chrome, Firefox. Try enabling/disabling worker mode in project properties.
Check in debug mode if webgl2 is enabled. If not, then all graphic tasks are handled by the CPU.