Show renderer caching status for the current page

Problem/Motivation

Besides showing the single caching status, which is super helpful, is it possible to indicate the general page / render cache status of the "master" page?

I'm not sure, if that's possible in all cases, for example with BigPipe, but would be helpful to directly see, if a page finally can be cached.
Is that possible, or are there any alternatives in Drupal already?

Currently, I only see the option to use curl -I which is okay for software developers, but for site builders something in the UI would be more helpful.

Steps to reproduce

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes