Executive summary: Write stories about things that have already happened in your world prior to the PCs' involvement. Cut those stories into bite-sized chunks and scatter them around adventure sites for PCs to find.
I've been playing a lot of Grim Dawn recently. Possibly an unreasonable amount. It's an ARPG in a "Victorian+magic" setting that has recently had an apocalypse. Grim Dawn's main story is... thin. It's kind of a checklist of "oh no we've discovered a new threat to the
surviving humans", with occasional choices in how to handle humans you
meet on the road. Most of these choices are reducible with experience
to their mechanical outcomes. In practice it's an excuse to go interesting places, vaporize monsters, and take their stuff. This is fine by me - never let a narrative get in the way of gameplay.
Where Grim Dawn succeeds at storytelling is in its lore notes. You find them scattered around the world and they give you many more perspectives on that world. The baddies plotting, your NPC allies realizing apocalypse is coming, refugees fleeing the capital, regular folks turning to dark powers to survive, stubborn farmers refusing to leave their land, a civilization collapsing to a previous apocalypse, all of this stuff that happened before the game starts is delivered to the player in written notes. It's the polar opposite of the exposition-dump; rather than getting a single long, boring account of the world from a third-person narrator, it's delivered in bits and pieces by a multitude of (sometimes unreliable and conflicting) in-world sources.
Grim Dawn does a couple things here that might be worth noting and stealing for tabletop RPGs. The first is that notes are short and often serialized. Rather than dropping a 12-paragraph story on you, they'll cut it up into four notes each of three paragraphs and scatter them around an area. When you find part three first and read it, and realize there's no closure, you know that there must be more before and after. It encourages you to explore the world to find the rest of the series of notes. It leaves gaps for you to speculate into - to imagine into. You wouldn't just show them the map - don't just show them the full lore! (Does it strain disbelief to have pages of a diary scattered over a half-acre? Maybe. Is it worth it? Probably, I think)
Reading lore notes in Grim Dawn also gives you XP. I don't know that this is quite the right thing for a game like D&D, but selling lore notes to an historian for GP, by which you earn XP? Hell yeah. Some players may be excited about finding lore for its own sake, some may need a more concrete reward, but as long as the table as a whole's reaction to finding a lore note is "score!" you're headed in the right direction. Make finding them gameplay, and reward that gameplay.
Finally, Grim Dawn is never pushy with the lore notes. When you mechanically "read" a lore note and get the XP, it gets copied into your quest log and remains available there. Maybe you only have an hour to play tonight and you need to grab that next portal, so you're not doing any reading. No worries, it'll be there next time when you've beaten the boss and are taking a breather in town to rebalance your gear. This is kind of a confident move on Grim Dawn's part; when a game makes you sit through cutscenes and exposition, it is because they're worried about what will happen if you miss something. Grim Dawn says "whatever man, if you miss a lore note or never get around to reading all the ones you do find, it's fine. My core gameplay is strong enough to bear it." Just so - don't read lore notes to your players like boxed text! Pass them a paper copy and make the page on the campaign wiki visible to them. If they want one guy to skim and summarize, fine! If they want to read it aloud, fine! If they just want to pass it to the one guy who cares about lore (who becomes the party archivist), fine!
Taken all together, Grim Dawn's approach to lore notes strikes me as an eminently appropriate attitude for lore-delivery in tabletop games, especially OSR games. In exploration-driven games, it is a given that players will miss stuff - you have to be OK with that anyway. In a game that keeps AD&D's apocalypse, having surviving lore in the written word rather than being able to ask people questions about the world makes sense. And stories about the past of the world don't step on the toes of player agency; you can have your well-structured narratives and character development, just separated from your emergent narrative by time.
In conclusion: if you must novelize, OSR DMs, serial-novelize the history leading up to the PCs, not their current actions, and scatter your serial in adventure sites.