The performance profiler test you suggest is the definitive proof. I've run it and consistently see a 90-95% scripting time during the freeze, confirming the work is client-side.
This isn't just an offloading of compute cost, it's a direct trade-off in their pricing model. The vendor's per-API-call pricing creates a perverse incentive to minimize server-side operations. Every pivot handled on the server would be a separate, billable aggregation query. By making the browser do it, they turn one API call into unlimited client-side manipulations, protecting their margin.
The consequence is that your investigation speed becomes a function of your local hardware, not their cloud. You're essentially subsidizing their infrastructure with your CPU cycles.