Make combat harder when it happens; XPs for social success
My brother does this. This experience-based answer is from an RP-heavy campaign that's been going on for over two years. We spend a lot more time traveling, exploring, and interacting with his NPCs than we do in combat.
We do a lot of role playing, not a great deal of dice rolling, as we go about meeting people, trying to find (and generally support) the true heir to the kingdom (there's a usurper who is I guess the Big Bad, and he's still in power at the capital) and along the way helping, for example, a village take back control of their brewery since the beer was going bad under current management.
- One of my favorite encounters was when our cleric, using the
tongues spell, got into a conversation with two hill giants and convinced them to let us pass rather than throw boulders at us: it
cost us two of the kegs of beer that were on the wagon and one of the
A couple of the PCs complained about that resource drain; I mean, we are talking two kegs of beer, darnit! ☹
- Our most recent session saw us neutralize an entire settlement of
wereboars without an initiative roll, DM awarded full XP for the lot of them.
If you have chosen high social, low combat, don't sweat resources
You are not being graded on how well you test your party's resource management skills. (Quite a few parties I have played with don't like that aspect of the game). That's how my brother handles it. Unless you choose to structure the game, explicitly, as the subgame of resource management don't worry about them. If your players don't worry about them, and you don't worry about them, that ceases to be a problem.
If your players, however, want more resources management play, then cater to that. (A couple of the other answers go into some detail on that).
IRL combat is dangerous to get into; reflect that "in universe"
Accept that PCs can die.
Don't pull your punches.
Yes, this may take another session zero to see if all of the players have buy in. (Some may not, our whole table is good with that).
I don't think we've had an encounter that was less than 2x Deadly or more in quite a while. Yes, that can lead to the complaint "15 minute adventure day" from an observer but the players at our table have responded to his approach well.
Focus on what your players respond to.
When combat does come, what I see at the table is that the players feel the tension immediately once initiative is rolled. I certainly put on my A-game each time we roll initiative. Lots of death saves, plenty of PCs at 0 HP over the course of the last few years, only two PCs lost.
Reward XP for social success
Here's a place that the 5e DMG falls down, IMO, and does not offer enough 'meat' for a new DM to nourish their DMing skills with. Assess social encounters as easy, medium or hard. (Deadly seems to not fit so far for us) and allocate XP according to that assessment commensurate with the PCs level.
After seeing him do this, what I do as DM when I have to sub in for him (RL is a thing) is I look at a typical adventuring day budget and create that many XP. Regardless of whether we have encounters that are social, or combat, or both that whole XP budget gets allocated to the players for the adventuring period. Sometimes, that may be a week depending on how much travel is involved, or it may be a day spent with the local noble and his entourage. Or, it may be a "15 minute adventure day" life or death fight with assassins coming out of the woodwork. 😮
His other technique is to have a lot of deadly stuff happen at night. Which makes sense; most assassins (and other nefarious sorts) like the cover of darkness. We, the party, seem to attract them!
It's not much trouble, I have found, to assign "easy, medium or hard" to a social encounter based on the encounter builder guidance. Most social encounters and role playing take a while, and dice rolls aren't that frequent.
Leveling by session count - another alternate that I'll mention
In a different campaign where I play, the DM does leveling by session count. Regardless of how much social, exploring, or combat we do, after three sessions "ding!" we level up. He hates the XP grind, and has a pretty open world. Some days we are grinding away investigating "what is the real problem here?" (intrigue is present in most areas we have been) and sometimes we end up in a battle once we figure out that is the solution to our problem, or we get ambushed/attacked/confronted.
This model may work for you. The current rhythm is PCs at level 1 for one session, at level 2 for two sessions, and from level 3 onward three sessions at each level. Did the PCs survive? Ding! If that is too fast for your story/world, he shared with me last week, when I asked him why he picked that rhythm, that his first campaign went 1, 2 at two, three at 3, four at 4 and all remaining levels. Campaign wrapped up at 12. He has been moving us faster on purpose to see if he likes the feel. So far, he's satisfied.
Our last session ended up with what was basically a prank pulled on an audience of thousands (not a combat encounter) at the end of my bard's performance -this after an entire session of social maneuvering and planning. Long story short: the queen is now a fan. 😁
Will this work for your table?
That depends on your players. They seem to like the social encounters you have presented so far. Do they like the prospect of maybe dying if they do have a combat encounter? If they don't, this may not work as well for you as it does for our group - feeling that quiver of uncertainty - "Oh, man, this just got violent" - adds spice to the game. Tastes will differ on how much spice a given table likes.
I'd also invite you to consider 3C273's approach, if you accept the frame challenge, even though
my players aren't really interested in trying other systems.