Cascading effect creates loss of performance

Proposed solution

I am unsure that _webform_token_render_more() is the root cause because the performance issue only happens when Search API is enabled.

I agree that it needs to be adjusted in the search api as well.

It's in both, as the core calls a render hook that triggers the hook in the search api, preventing the render from being called unnecessarily is important.

This render in the webform is called even if it's not on a webform page or in the webform admin. All it takes is for some module to invoke the tokens that arrive in this function.
However, in the search api, I agree that there needs to be a rule to prevent unnecessary processing. I'm still investigating how to patch it.