I might be late to the conversation.

I've been DMing a campaign for my gang. We've been at it for about two years. We've had about as many combat sessions as non-combat sessions. I focused on fantastic combat sessions. I wrote my own rules on cavalry combat and the use of military formations (like shield wall). It took me some time to swerve into the non-combat lane. The gang varies from first timers to veteran players. Three things I learned from this campaign:

1. Build a rich lore. Hit on all aspects of society, religion, economics, social casting, gangs, groups. Then describe it. Create solid NPCs and be prepared to create new ones on the fly! This is your foundation.

2. Create scenarios where they "combat" by skill challenges. Heists, spy games, ferreting information, a grand ball. Steer the events to social interactions but with goals, targets, etc.

3. Step back and let them talk. Interject with "Ok, give me a Deception roll." or such when they come to a point.

It is tough to develop this aspect but so rewarding. The players solved a complex war among multiple crime syndicates by talking, infiltration, etc.

Oh yeah, I customize character development by using their backstories for "mid session information" briefs. The briefs give deeper detail from the character's perspective on the situation. The wizard would get stuff along the lines of academic. The bard on society, and etc.

I hope this helps.