As you've already figured out, character focal adventures cannot be set up in the same way like a dungeon crawl or an event path - all you can do is provide some starting point material that makes it easy for the GM to improvise and fit to their own group.
A Common Situation
You can start with a general situation that the adventure/scenario is about. This puts a loose requirement on the unnamed PCs but usually a fairly easy one - "There is a struggle for the throne - you have to have a vested interest one side or the other winning.", "You are all generals or high officials of the daimyo... who just died the night before battle. His heir is 3 years old." etc.
This sets up some general problems while leaving the individual characters open.
Ideally, you're playing with an RPG that already has good Flag mechanics built in. Either way, you should make part of the set up for the adventure, a few questions that define the characters in relation to the situation.
For example, with the daimyo example, I had players answer these 3 questions:
- What are you most renowned for?
- What is your ambition?
- You failed the lord in some way. How?
Even though you may not know who the characters will be, a good set of leading questions allows the group to focus their characters to the situation and gives the GM a good set of handles by which to grab onto appropriate conflicts.
You can create a set of NPCs that have whatever stats you need, a basic motivation or general personality for the situation. The GM then takes the PCs the players made as their inspiration to alter the NPCs to better create interesting conflict. This can be as simple as just having NPCs who directly oppose the PCs flags/established motivations, but it can also be based on the answers the players gave to the leading questions. NPCs with their own goals may align or conflict with the players pretty easily - my Seven Types of Antagonists give good options.
Alternatively, you could also choose to have a sizeable Conflict Web of NPCs in conflict to which the PCs, being involved in any way, will probably be opposing someone or another.
Nailing it down a bit more
You can, also put additional requirements on PCs while leaving 80-90% up to the player's preference as far as character creation. Good options might include requiring a motivation or Flag of your choice (the game Tenra Bansho Zero has the GM give a Destiny to each character after their intro scene, for example) or putting in required NPC relationships ("Someone here has the Prince as their lover.").
Now Writing It
Obviously, this depends on who you're writing for. If you're writing for yourself, you can simply use the ideas outlined above and run the scenario/campaign - this is what I usually do - prep, players make PCs, minor tweaks (often during play) and go. If you're writing for others, this isn't so bad if the game already gives a lot of structure or advice for focusing on the PCs as the point of play (usually, Flag mechanics, narrativist game designs, etc.). If the game doesn't, I've found often people don't recognize the material as an actual scenario/adventure, because they're either looking for a map or a list of events to be included.