Hi Richard and Chris,
An easy way to find examples of plugins that do store user info is to go look at your site, Plugin privacy compliance registry. In Moodle 3.4 prior to the current build it is at Site administration > Privacy and policies > Plugin privacy registry. For the latest current build of Moodle 3.4 and the current code for Moodle Beta 3.5 it is located at Site administration > Users > Privacy and policies > Plugin privacy registry.
Anything listed with a + in front of it has some sort of GDPR implementation. Knowing that, makes it easier to go directly to a plugins code to look at an example, instead of hunting through all the plugin folders, one at a time.