Is there a standard place 3rd party module pages report what PHP version they're tested on? Is this info reported anywhere?

for e.g.
https://www.drupal.org/project/optimizely

or

https://git.drupalcode.org/project/optimizely
There is a route for all modules of the pattern https://www.drupal.org/node/{nid}/qa for showing testing reports.  Nightly runs, per-commit runs, and one offs should appear there.

For the module you mentioned, the page is https://www.drupal.org/node/1305958/qa, and it looks like automated tests aren't set up.

The Poll module does show tests, https://www.drupal.org/node/1896974/qa

In general, the default test (if set up) will track the min versions for PHP and MySQL for the chosen core branch.