Improving Combat

Make combat lethal by increasing damage and reducing HP (for players and enemies). It will also encourage players to plan ahead and actually care about getting hit.
When the players gain significant advantage - enemies can run away, beg for mercy, try to negotiate, offer to betray their master, etc.
Allow instant kills. When players come up with a brilliant idea or a super exciting move - let them have their moment, don’t make them roll for damage, let them defeat the enemy in one awesome move.
If you notice players getting bored or running out of cool ideas to try, then fudge the numbers and get it over with.
Use a timer. Give players 1 minute to decide and describe what they do for their move. This adds tension, and encourages players to plan their move while the others are taking their turn, maintaining engagement.

Make action scenes interesting the same way writers/screenwriters do:

Make it dramatic, meaningful to the characters and to the story, create high stakes and important consequences (Luke fighting his own father, Frodo vs Gollum in the Mount Doom).
Create cool set pieces that put characters in unique/interesting situations (fighting on the roof of a moving train, collapsing buildings, on top of a blimp, Jack Sparrow fighting on top of the mast, Inception Hallway fight, Mad Max, etc.)
Make vivid and cinematic (but concise) descriptions. Read screenplays for great examples. If you’re not using a map - make it clear where everyone is in relation to each other.
Take inspiration from books and movies, just copy great action scenes.
Don’t do unmotivated random encounters with generic monsters - it’s boring and meaningless. Have fewer but more powerful and interesting enemies instead of a bunch of identical repetitive ones.

Make the environment interesting the same way level designers do:

Create environmental obstacles/hazards (traps, lava pits, rockslides, stampedes, storms).
Give players opportunities to creatively use their environment (drop a chandelier onto their enemies, set loose wild animals, create a barricade, Jack Sparrow vs Will Turner fight).
Use Terrain with Elevation (cliff, waterfall, ravine, raging river), difficult terrain (mud, slopes, swamp) and Cover (columns, tall grass, boulders).
Add Interactable Objects (stalactites, chandeliers, wagons, oil lanterns, curtains, explosive barrels, catapult, single use hand grenade).
Allow players to impact the environment - fire/ice/water surfaces, create clouds of smoke.
Make setpiece matter, add environment-related events during combat that demand a response (a wave hitting players and washing them off the ship so they need to climb back on, boulder falls into the river of molten lava causing it to splash over the battlemap).

Prompt players to describe their actions. Ask “What your attack looks like?”, or more specific questions - “How do you want to engage this creature?” or “How are you planning to get to your ally who is surrounded?”
Encourage banter between players and NPCs during the fight. Give the enemies personalities and desires, make them relatable and interesting to talk to.
Let players contribute their own ideas, add to the environment. When player asks “Is there a tree somewhere? Or any solid vertical plane?” “Is the cave floor smooth or rugged?” it means that they are thinking of ways to interact with the environment. Whenever a player asks “do I see X?” to almost always say yes. If a player comes up with a cool idea - encourage it, let it happen.
Give players or enemies an objective that does not involve direct violence(get the injured NPC out of the dungeon, end the combat quickly, run away, avoid injuring innocents, steal an item and escape before more guards show up, do it stealthily to avoid attracting more guards, disable an alarm. The enemy might only want to complete the ritual or take an item from the players, the monster might only want to protect it’s eggs).

If you’re the GM and you want to encourage more narrative creativity - start with yourself, get creative with the combat narration as it happens.
Try to offer interesting/creative/difficult choices every turn. That’s what makes it engaging. Create consequences for the choices to make them feel meaningful.
Give NPCs unique and interesting powers, abilities, tactics.
Don’t put the story on hold. Reveal interesting/useful information about NPCs or the story, create character development moments.