In fact the Pynecone frontend is built statically. But UI event handlers are run on the backend. The latency scenario is identical to if you used HTMX or Hotwire or a traditional web server. You click, it gets posted to the backend, an output comes back and is rendered.
The click counter thing is contrived and maybe Pynecone should have avoided centering on that, since the users they're targeting for sure don't care about frontend-only click counters.