Main picture: A Handbook of Rome and the Campagna
When it comes to running any tabletop RPG, be that D&D or Numenera, Call of Cthulhu or Paranoia, the touchstone for you as a GM has to be this:
Keep your players engaged with the story
Everything else comes from this foundation. If your players aren't engaged, then they're not going to be having fun, in which case they may as well not be there. Their characters have to have a stake in what's going on. Obviously, the methods you use to create that also need to reflect the theme of the campaign and the overall story, as well as setting up character arcs.
With that in mind, you need to be doing two things: creating a compelling campaign story, and pitching the players against a compelling adversary. The first of those I've written about before, and you can click that link to read my thoughts on it. The latter is what we're looking at here.
Powerful Moments Require Connection
The first way to create great engagement is to get the players to interact with the world around them, creating moments of connection with other characters. If we look at the Titansgrave series, we see a particular moment in episode four where one of the characters encounters a moment of tragedy. This is a moment where the entire group are visibly nervous based on what's happening. The resolution of that situation also has emotional pay-off, but none of it would work if not for the attachment the players have to the circumstances of the moment.
This is why it's not enough to simply have a random NPC be dead in a road. Simply encountering that isn't something that the players are going to care overmuch about. However, if that dead body is related to a character, or you use it to introduce the person's parents and let the players interact with the grief those people are experiencing, that can be a deeply powerful thing. Equally, if the party are attending a wedding and asked to give a speech, they're not going to be able to do that and impart anything meaningful if they don't have a connection with the people being married. However, if it's an NPC that they've been interacting with for a while, or if it's one of the other player characters, then that can have significance to them.
Great Villains Covert the Player's Goals
The second way to get players engaged is to get them to interact with a villain. Now, if you're putting an overarching Big Bad Evil Guy (or Girl/Demon/God/Creature) into your campaign, that villain is only going to be as compelling as the force they're able to bring against the characters in the story. Note that I didn't say physical violence - although that is obviously one way to push against the characters, it's far from the only one. The aim here is to take the character's goal, and have the villain want the opposite of that specific thing.
The best way to go about this is to talk to your players about their characters off-screen, and get background information on them. If the character fell out with their parents and is seeking reconciliation, have the villain use that against them by turning their parents against them, or hurting them and making the character see how powerless they are to prevent it. If they are a recovering alcoholic, use that to hit the character with torment over their lack of self-control and their weakness. If they had an unhappy childhood, hit them with how alone they were and how no-one ever really wants them around or likes them. Even psychopaths have weaknesses - take Amos from The Expanse. Here's a character who's completely devoid of a conscience. But he recognises that, and wants to be a better man, and so his central conflict is his battle with himself to do the right thing. To make good decisions. Thus the greatest villain he faces is himself, when he makes the wrong choice.
A villain doesn't have to be an external thing - in narrative terms, it's simply the thing that stands between the player and their goal. The better you can make the villain at hitting the character's greatest weaknesses, the greater the tension will become between the character and their goals, and thus the more powerful the resolution of those things will be. Therefore bringing the players into situations where they become more invested in the narrative.
Character's Tests of Character
The final way to create great player engagement is to get them to engage with their own character. And the beset way to do this, is to apply pressure.
What we're aiming for here is what Aristotle defines in Poetics as anagnorisis, that is:
The discovery of one's own identity or true character, or of someone else's identity or true nature by the tragic hero
Great moments of this from contemporary works include the realisation (from the character's points of view) that Darth Vader is his father, that he's dead (The Sixth Sense), that some villains can't be reasoned with (The Dark Knight), and... well, there's just so many in the Lord of the Rings films I'm not even going to start listing them.
There are two main ways to create these types of situations. The first is by applying great pressure to the players and their characters, in moments where they must choose. Under the pressure of choosing, we see the players have to weigh up those options in the mind of their character. The harder the choice, the more the player will learn about their character in that moment of decision.
The second is to hide something from the characters (and possibly players too), which is of special significance to them. That way, upon the discovery of that thing, they encounter a moment where they as the player must process that thing, and what it means to their character. This again involves getting into the mind of the character and mentally role-playing the experience. This also forces the player to empathise with the character they control, building the character in their mind and in the minds of the other players, again creating engagement.
Obviously these things cannot be done all the time, or even to all the players in one moment. It's not impossible - the death of a beloved party member, or the loss of something particularly meaningful or an impactful failure can affect everyone at once. But through repeated small moments and time, you can build empathy in the minds of your players, and bring them, through the story, to powerful, emotionally involving moments.
Equally, this shouldn't be a way to simply beat the players; it's not a "feel something!" stick. These are tools to draw people in, not ways to punish them needlessly.
Their engagement with and enjoyment of the story is fundamentally what everyone comes to the table for, and that's what you as a GM are there to do:
Create a great story, and bring the players into it.
Hopefully this will help you get a little closer to that.