Gosh. You made that sound complicated. 
Ostensibly, you pop the fixed tag on bugs that have been fixed and completed on feature requests that have been implemented. [1] It’s part of the process to close the topics out (and keep interested parties updated with the relevant info). They were initially implemented to provide some visual indication that ‘a good thing had happened’ versus the lock symbol of a closed topic. When these tags are consistently applied you get a nice wave of green when you scroll down their category topic lists.
(And delivered was a separate but similar one that wasn’t team—controlled so it could be used in Marketplace)
For Solved, there are quite a few categories where it’s active rather than just the generic Support category. Pretty much any category where the majority of topics are going to be questions that can get a solution. Support, Installation, Dev, Data & reporting, SSO
Ideally, the best practice is to have the OP mark the solution but we know that this sometimes doesn’t happen (for a variety of reasons) so I would often scroll the topic lists back and clean some outstanding ones up after a couple of weeks or so (once they were deemed to be ‘abandoned’)
FWIW The Theme component topic for that is Reader Mode, so really that feedback topic you linked shouldn’t be in Theme component (as it’s not a theme component topic). It should probably be in Feature or UX as I think that’s where these have come to live now more of them exist.
(I think it was in Site feedback as it was an experiment here on meta)