The rift, the crystal tower, and the seat of sacrifice (Spoilers up to 6.0)

[Lyth]

I think you're better off thinking of FFXIV's story as modular. The MSQ is designed to keep you up to date with the essential plot events while getting you into the gameplay. It's already fairly cutscene heavy, so if you added more story content to it, people will get overloaded with information and will be more likely to skip through it. That's why the Unending Codex was likely added, to give such players an easy way of understanding the core plot without having to remember a lot of additional details. If the story is really important to you, however, none of the 8p raids are really 'optional' or 'side content', and all of them end up having tie ins to the MSQ in the long run.

If you think that missing the Alexander storyline is bad, both the Coil and Eden stories have an even bigger impact on the plot. Coil has hidden away a major cutscene explaining the true events of the Seventh Umbral Calamity, and Eden has a significant amount of lore about the First, Thirteenth, and the Ascians, including some fairly interesting commentary on utopias from Mitron that sets up the main themes of Endwalker. Not only that, but the many of the boss designs and mechanics have subtle bits of lore behind them as well, such as Cylva's sword in E10S, E11S's boss design as a curious hybrid of Ran'jit and Thancred, and the Savage-exclusive second phase fight against Loghrif in her true form that references your earlier fight against her in E2S as well. If you're at all interested in Void magic, it's a pretty amazing series. And to think that Pandaemonium is likely going to be even bigger than this in terms of lore impact.

In short, it's all important! The only thing that I can say is truly 'side-content' is when you try to clean out random '!' marks from your map, but you can find surprises lurking there as well.