How would people structure a session without combat as the focus?
There's several approaches, but let's try working with what D&D already does typically.
Imagine a simple dungeon. The PCs are told that there's loot, or some goal, at a location - they go and explore the dungeon. We can start with a really basic idea - each room contains a monster to fight, and a treasure to be taken. An interconnected collection of Orcs and Pies.
A less basic (and more typical) situation is that some of the rooms have monsters, and others have other types of challenges - weird puzzles or physical situations the PCs have to bypass to get the treasure.
Next, replace
all the monsters with other challenges.
Next, replace "dungeon full of rooms" with "chart of people and places the PCs can interact with". Instead of Rooms 1, 2, and 3. We have Bob, Sally, and The Town Library. You can go to any of these places, face some difficulty in attaining a goal, and then go to the next. Eventually, after workign trhough a goodly part of the chart, the PCs find the end challenge, and gain the Big Reward.
Form that as a 5-room dungeon, and presto, you have a session without combat as the focus.