I'm going to gloss over the salt in your post and toss off a couple of ideas. In the Dresden RPG, building the city that will be the primary setting for the game is done collaboratively. All the players and the GM take on some sections of the city and building some of the fiction fiction about how they work, who the important people are, and how it connects to the rest of the setting. This allows players to build specific foes or concepts into the setting that they're interested in, and also allows for a better level of area knowledge and also more investment in the setting from the players. The GM takes that initial work and sands off the rough edges. It's awesome for a sandbox urban setting.So go ahead. Give us some advice on this subject grounded in D&D 5E.How should the players be equally responsible? In what way? I just spent four hours making my groups next adventure. How do I get each player to put in there four hours?What do they spend that time doing? How does a player become equally responsible?
An artifact of current RPG design that appears in 5e and mostly doesn't get used, or used to great effect, is the Inspiration mechanic. Mostly because it's a crap mechanic really, but also because it feels bolted on and not terribly useful. However, what it is the most like is some of the mechanics from games like FATE that are designed to leverage the characters' motivations and goals to drive the engine of the fiction. If you buff those rules up, and leverage them harder, both during character creation and in-game, the result at the table is something closer to FATE if you get player buy-in, which is more character driven decision making and pulling player agency to the front of the game, which is useful is a million different ways. To speak directly to your question the increase in character agency tends to mean the characters are more focused on actual goals of their own rather than just following the trail of breadcrumbs left by the DM. This can take the narrative off on lots of different interesting paths where the DM can just let the character decision making drive what happens next.
Exactly what that above idea looks like at an individual table will depend on your goals for the campaign. You can use more or less FATE (or whatever) depending on how much sandbox you want. The stronger the characters the cooler sandbox games tend to be. What D&D lacks is any real motivation for the player to build a really strong character with a well defined set of goals and motivations. Other RPGS have some great tools to make that better.