I do find it a bit wild that people find 4e D&D narrativist. Like sure, if I squint really hard, I can see the points raised, but those seem to be more in the eye of the beholder rather than in the game text. For example to me the "player authored quests" is simply advice to award XP for unplanned stuff the PCs decide to do and nothing more. And what is weirdest to me that many of the people who seem to think 4e that way also seem to think that 5e is super bad fit for narrativism. Eh. They're different but ultimately pretty similar. The biggest difference is that 4e is way more combat focused and absolutely requires detailed battle maps to run properly. It is more gamist, than 5e, that's the actual difference.
I don't know how you are using "gamist" here. Not in Edwards's sense - perhaps in some bespoke sense of your own?
I also don't know why you seem to think that a focus on combat as the key site of crisis and climax - the crux of the rising conflict across a moral line - is at odds with narrativism. There's plenty of other forms of fiction where combat plays that role - I don't see why RPGs would need to be differently, especially given their wargame heritage.
The salient differences from 5e are multiple. Some key ones are: 5e PCs are on a "daily" recovery budget, which means that the scene/encounter is not the basic unit of play; 5e PCs are on asymmetric resource and recovery frameworks, which push against the GM just framing and resolving without curation; 5e DCs for non-combat resolution are not set on a "pacing"/'rising action" basis, whereas 4e's DC-by-level chart achieves this.
On player-authored quests, they are not what you describe them as. The PHB (p 258) sets out the idea of a quest, and the contrast between a GM-authored and player-authored quest:
Sometimes a quest is spelled out for you at the start of an adventure. The town mayor might implore you to find the goblin raiders’ lair, or the priest of Pelor might relate the history of the Adamantine Scepter, before sending you on your quest. Other times, you figure out your quests while adventuring. Once you assemble clues you find, they might turn into new quests.
You can also, with your DM’s approval, create a quest for your character. Such a quest can tie into your character’s background. For instance, perhaps your mother is the person whose remains lie in the Fortress of the Iron Ring. Quests can also relate to individual goals, such as a ranger searching for a magic bow to wield. Individual quests give you a stake in a campaign’s unfolding story and give your DM ingredients to help develop that story.
The first paragraph describes quests as a technique for GM-driven play. The second paragraph shows how quests can be used as a framework for player-driven play. The DMG then elaborates (pp 102-3) :
Quests are the fundamental story framework of an adventure - the reason the characters want to participate in it. They’re the reason an adventure exists, and they indicate what the characters need to do to solve the situation the adventure presents.
The simplest adventures revolve around a single quest, usually one that gives everyone in the party a motivation to pursue it. More complex adventures involve multiple quests, including quests related to individual characters’ goals or quests that conflict with each other, presenting characters with interesting choices about which goals to pursue. . . .
The goal of a quest is what the characters have to accomplish to succeed on the quest. Goals should be as clear as you can make them. Goals can change as the characters uncover information, but such changes should also be clear. . . .
Quests should focus on the story reasons for adventuring, not on the underlying basic actions of the game - killing monsters and acquiring treasure. “Defeat ten encounters of your level” isn’t a quest. It’s a recipe for advancing a level. Completing it is its own reward. “Make Harrows Pass safe for travelers” is a quest, even if the easiest way to accomplish it happens to be defeating ten encounters of the characters’ level. This quest is a story-based goal, and one that has at least the possibility of solution by other means.
Conflicting Quests
You can present quests that conflict with each other, or with the characters’ alignments or goals. The players have the freedom to make choices about which quests to accept, and these can be great opportunities for roleplaying and character development.
Player-Designed Quests
You should allow and even encourage players to come up with their own quests that are tied to their individual goals or specific circumstances in the adventure. Evaluate the proposed quest and assign it a level. Remember to say yes as often as possible!
Most of what I've quoted from the DMG talks about how quests establish PC goals that provide a reason for adventuring. It also explains how conflicting quests - that is to say, goals that are to some extent at odds - provide opportunities for conflict (
rising conflict across a moral line!). And then the last paragraph I've quoted encourages the GM to put this onto the players - thus establishing player-authored rising conflict across a moral line.