Combat is honestly one thing I feel the weakest in as a DM. Running all the different monsters, tracking status effects, and abilities can absolutely turn into a slog quickly if I let it, so I have tried to add in story moments to every fight within reason.
Now what does that mean exactly?
Well, it can mean the players seeing an enemy mage casting fireball and not caring that she blasts several of her allies, leading to in-fighting and arguing in the middle of a fight. It could be noticing that one monster seems to always be standing in front of another monster and that maybe the two of them are connected in some ways. In one case, it meant Moonbeam being cast on an NPC and revealing his shapechanger nature and true form in the middle of a fight.
Fights are often about passion, danger, and struggles, and that can show a lot about the people in the fight.
Let the enemy soldier put themselves over a hidden trapdoor, knowing their death will hide it from the players. Or show how the pirate captain orders her second to retreat and save himself. Showing moments of humanity or strangeness makes the combat more interesting and can adjust how the entire fight runs.
It also, for me at least, makes the fights more interesting. Instead of being about stat blocks and abilities, it’s about what these characters want and will sacrifice to make it happen. A desperate wizard casting a fireball centered on themselves to take out the barbarian says a lot about the character in a way that a monologue never could.
The important thing is to remember that you, as the Gamemaster, should also enjoy your game, and that sometimes means adding in different things that you enjoy. If something feels more like torture than a joy to plan out or run, then something needs to change for you.
Find the things you like the most and incorporate those into your game. Keep your world a living, breathing, strange beast that you can adjust to fit the campaign, the players, and yourself.