You've got your final mix as a stereo file so now you're ready to "master" it. Mastering just one song on its own is mainly like mixing except you've only got one (admittedly stereo) track. You set its volume and maybe apply some EQ and compression to get the desired result.
Where mastering is interesting is when you're mastering a collection of songs, such as an EP or an album. Then, the purpose is to make sure that the different songs sit well with each other. Even if they're part of the same project, they may have different sounding mixes because different techniques were used or just simply because there are different styles e.g. a hard rock number followed by a softer ballad.
You don't want the song transitions to be unwittingly jarring (you might want to do this wittingly for artistic reasons) so again you can balance their respective volumes and EQ to help the flow. The difference with mixing is that in mixing at least some of the tracks are usually playing simultaneously, while you master the songs in sequence.
While there are still artistic decisions to make at this stage (e.g. how long are the gaps between songs? How loud should one song be relative to another?), mastering is a more technical exercise. You need to think about the final medium and its constraints e.g. making sure that you retain dynamics and reign in deep bass for a vinyl master. In fact, if you're going to release on multiple media (CD, vinyl etc), then you may even do separate masters for each! I suspect that this is probably why many people prefer vinyl: since the medium can't physically handle super-loud, squashed, masters with massive bass, you have to master with a little bit more taste. If you listened to the same master digitally, it would sound just as good.
We don't pay much attention to the so-called "loudness wars". Ultimately, people are going to listen at whatever volume is comfortable for them and the last thing you want is to force people to turn the volume down as soon as your song comes on. Talk about self-defeating! Streaming platforms also do their best to normalize volumes between different tracks so they'll just turn your ultra-loud master down automatically.
Our approach, for "loud" songs at least, is to find the "natural" loudness of each song, where going any louder starts to damage to the overal audio quality by introducing noticable artefacts (e.g. distortion), and leave it there. For EPs and albums, we do this for what should be the loudest song first and then set the relative volume of all the other songs accordingly. If that's quieter than what others are doing, then so be it.
We doubt if anyone can accuse our music of being too quiet!