Wanna disclose that the only ttrpg I've played in depth is dnd 5e, so other systems might offer interesting answers.
TLDR I want to make combat more interesting as it progresses, not less
So combat in dnd is what should be the coolest and most entertaining part of a story, but is often the slowest part of a session. Most of combat is spent waiting for your turn. When it is your turn, sometimes, you'll swing twice with your sword, miss twice, and that's it, that's all you can do. Even when you hit, the consequences are often just an invisible number going down. Not very interesting, there's next to no input from the player, and this is mostly just the dice deciding everything. No room for roleplay or storytelling here.
So how, from a game master's perspective, can we make combat more interesting? A straightforward solution is to just have a bit of story content in each turn. Describe a fighter missing their attacks as "you are locked in combat with a warrior, who narrowly blocks your blows. The sound of steel on steel rings through the battlefield." Doing this for every turn is exhausting for the DM, where they have to try to give a flavourful description for everything, but every now and then can give more vivid images to your players.
Dialogue is another way to insert storytelling into combat. I've seen no DMs ever enforce the "6 seconds of dialogue per turn" rule in dnd, because it just sucks. Have the antagonist exchange barbs or shout their ideology at the players. Have them discuss their past with the player. Describe it as them shouting at each other over the wind, or the sound of war around them. Again, this can't be inserted into every turn, or it too will become monotomous.
So what about mechanical ways to elevate a battle? Legendary actions in dnd serve this purpose, to allow an NPC to perform actions when it isn't their turn. This helps to alleviate the action economy problem and makes the NPC seem a lot more active and dangerous. If a boss can attack when you don't expect, it makes the mechanics fade back into the background a little bit as your players realise how powerful this character is.
I think debuffs are the most frustrating thing to happen to players. Being able to do less without any long-term change to your characters is just annoying. Getting disadvantage on an attack means your character is less impactful in a session. As a player, this sucks. Imo, debuffs should be avoided unless they either apply to everyone fighting, including your enemy, or they advance a character's story. My DM actually achieved both of these scenarios. They designed a combat encounter where difficult terrain was cast by an opposing spellcaster, and their fighter and ranger could navigate difficult terrain easily. This made us realise that the enemy had planned their attack to our specific environment (forest) and that they were particulary dangerous in this specific location - but if we meet them again under different circmustances, they will lose their advantage. In another encounter, one player, who's character has been lacking control of their own life, was suffering massive debuffs from a character who was trying to control their mind. They had to make saving throws every turn, but the stakes were a lot higher than just missing the next attack - losing a saving throw could permanently change their character.
Debuffs are hard to pull off, but buffs aren't. Imo buffs are the easiest way to escalate a fight - have your NPC become stronger and more dangerous as a fight goes on, rather than them losing resources like health and spell slots. Have your NPC become stronger after losing a certain amount of health, or even have a second and third phase with different attacks and new descriptions - this makes a boss fight feel much more tense. You could also give your player a weapon that becomes stronger after landing more hits or something, or an accessory that halves their hp and gain advantage on every attack. This makes them feel like they're becoming cooler and more powerful as the fight goes on, too.
Are there other systems that better escalate combat? I find that combat in dnd becomes more predictable the longer it goes on due to the system of health and spell slot attrition. Characters in a fight only lose resources, but don't become stronger at all. A lot of power fantasies have fights become bigger and more bombastic as they go on, because that's fucking cool, but that doesn't happen by default in dnd unless you try to make it happen. So do other players or game masters, or anyone with experience in other systems, have anything to weigh in on? My ideas are just ideas and I haven't actually tested these, so I would love to hear from others.
this ended up being a lot more text than i intended.
Barrach O'Bama is a deep state Celtic sleeper agent