There are 2 central design questions here:
1) How much does it matter that the game do this?
2) What's the best way to make that happen?
Here's what I mean: if an enemy uses "flurry" - which perhaps gives it a damage buff and a defense debuff, or a damage and speed buff, or any kind of combo of things - the player doesn't know what this does though. If you use a pop-up effect of like "+atk +agi" you get some idea, but you are still lacking a lot of info... a +20% buff is like, ok, maybe that'll change my decision in some situations, but a +100% buff will DEFINITELY make you want to guard, or heal, or take some kind of action that you wouldn't have otherwise.
From my perspective as a game player:
I've never needed a game to tell me, flat out, exactly what the buff does or by how much. Short of the game being competitive in some way. Or, there are two similar skills that do the same thing and I need to know what the difference is.
If the game simply puts an icon on an enemy that denotes something beneficial to them, then that's usually enough.
However, here's where this will get muddy.
I'm so used to playing RPG's where the "status effect" is basically meaningless, that I ignore it unless it is particularly detrimental. A 25 or even 50% increase in attack power from a boss is usually "minimal" at best. Heck, in a good chunk of RPG's, a 100% boost in attack power is basically meaningless to me, as a player (looking at you Mega Evolutions in Pokemon and Gigantamax! Where the only place these matter is competitively since these boosts are basically meaningless when coming from the AI!).
Let me put this in perspective. I play Final Fantasy XIV. MMO game. Lots of status effects in it. All through the game. You got some "consistent" ones, but, there's a lot of just... not consistent ones. In most fights, I don't care what buffs the enemy has on them. They're just not all that "game changing". Doesn't change the gameplay from "tank and spank without thinking". It just changes it to, "might take a little longer" or "healer might have to heal 2 or 3 more times than normal in a fight".
But, I was running some world events yesterday to grind for a particular item (game calls them FATEs, you walk into the circle, click the "level sync" button, and then do the event and get rewards for it). I ran across an event I hadn't ever done before. Some boss monster thing in a low level area. Well, my stats are basically off the charts anyway, so a sync of my level doesn't mean much.
Partway through the fight, the boss monster did some self buff thing. It lasts 30 minutes... the FATE only lasts 15. Normally, I don't care what the buff was. Except... I had to. It effectively cut my damage down to 1/4 of what I'd normally do. I went from hitting 400's to 100's. On a boss with a time limit.
I understood IMMEDIATELY what this buff did by just pure observance of it in action. It also MATTERED what the buff did because of the timer.
So, from my perspective as a player, I didn't need a tooltip or anything. I didn't need the game to tell me in words what the buff did. I didn't even need it to tell me the implications. I understood immediately. I had less than 15 minutes to kill this boss, and they just cut my attack power by 1/4.
So, unless your buffs or debuffs are going to be doing something I can't easily understand within moments, I don't need an explanation. This works the same with skills in games. If I get hit once with it and can immediately see its effects, I understand the implications immediately. This boss hit me with an attack, it ate half of my HP, so now I know to defend against it next turn. Or interrupt it. Or heal after it. Whatever my options are.
Another example: a boss uses something like, "command minions" - let's say this gives all his minions +50% atk for the next turn. Again, you're not really sure what this skill does.
I'd just have it put a little "attack up" icon on them so the player knows. Then the esoteric nature of the attack is communicated better.
But, this will require you have some consistency in what the icons look like and communicate. If the player knows that icon is always a buff to attack, then when they see it, they will react accordingly (hopefully... as long as the buff actually matters... because if it doesn't... the communicating what it does is utterly pointless).
So the first question is - maybe it's ok to just let the player figure this out through playing the game? That seems wrong to me, as it can be frustrating to not understand what's happening in combat. So the second question then is - how do you make it clear to the player what the enemy's skills are doing exactly?
To answer the first question:
I prefer if the game lets me figure things out on my own most of the time. Unless something can't be easily inferred, I don't really need to be babysat. In the same way I rant about tutorials, I will rant here about this. I do not need you to tell me that left joystick moves me and right joystick looks around. This is the common control scheme across nearly every game on the market right now. The first thing I do with any new game is press every button to see what it does in the game. So, I don't need you to tell me "press trigger to fire!" and "press A to jump!".
Likewise, I don't need the game devs telling me, "The enemy has this buff now, that's bad!". Especially when it could be a lie. Maybe you THINK IT SHOULD BE bad... but maybe I'm so far over leveled that it isn't bad. Maybe I don't care and never will, because the buff or skill doesn't matter to me. I can assess how good or bad a buff or skill is on my own, and if we're honest, I won't know if it's good or bad or irrelevant until I'm hit with it.
My example of that is just always going to be Final Fantasy 13 where they made a huge deal about the "Break Gauge" and how you had to do all this tedious crap to interact with it and such.
Meanwhile, before even the midpoint of the game I'd found a way around ever engaging with the mechanic and was killing enemies FASTER without worrying about it. So... the 30 tutorials or whatever that existed about it were largely a waste of time.
So, what do I need you to explain to me as a player? The stuff that isn't easy to intuit. I'm not going to figure out that holding left bumper and hitting A at the same time does a new skill. Not unless there's some context clues like holding the bumper opens a new menu. If I don't know that I have to throw 3 potions at the enemy, then have half my party use Defend while one uses Poison and the other buffs them, in order to win... then you should probably tell me that.
Now, please keep in mind that I'm probably a "veteran" game player. My advice on the subject of tutorials is not helpful if you have players who have never touched a video game before. Especially those unable or unwilling to experiment and try things and have the brainpower to work things out for themselves. My suggestion will actively hurt those players and their experiences. But, this is just how I feel about tutorials and overly explaining everything to me as a player. I need an explanation when it's not easy to figure out or intuit. That's all.
As for the second question:
Consistency. I do this in my own games.
There's Poison Level 1 through 4. The icons are different for each. It's a Poison Cloud around a person in all of them, but the last one has the cloud change color. Oh, and there are a number of stars to indicate "severity" of the state. Each state works like this. The enemies apply the consistent states. The "inconsistent" states are all ones the player inflicts... and they're explained by the attack itself. Or, if not explained, easily inferred.
Enemy quirks are explained by NPC's most of the time. At least, if they're not easily inferred. The "Revenge" mechanics are explained by the NPC's pretty early on. The player has a chance to see them in action. Likewise, these moves aren't designed to "kill", but merely to "hinder". So, they are consistent in their implementation.
Skills that enemies use will be told to you by NPC's in the area, most of the time. That way, when the player sees it, they can recall the information they got, and apply the correct strategy to dealing with it.
It's just about having all the mechanics stay consistent, so that everything is communicated effectively. It is also about letting the player know ahead of time, that maybe there's a new mechanic at play or a twist on an old one.