Cleanup some public headers and mark gs-test.h as public

These have come out in the process of adding tests similar to those in GNOME Software to an out-of-tree plugin (APK plugin, currently used in Alpine and postmarketOS). Some public headers couldn't be imported because of referencing private headers and the gs-test header is not considered public, which is inconvenient.

This is mostly a feature request that would make our life easier and increase the quality of the plugin if it is ever merged :) In case this cannot be landed for whatever reason, do you have some recommendations on how to approach this problem? Also, I only have a very rudimentary first WIP patch for the tests in the OOT plugin, so I guess there is a chance of some follow-up MRs if more problems appear.

Currently, the build is failing because some plugins seem to make use of functions which are defined in a private header. I wasn't sure if the better solution would be to move the necessary functions to public headers or to add the private headers to the plugins (as that might be undesirable). Let me know which solution is best and I can work on it.

It would also be super convenient if this was approved to be backported to GNOME 41.