I'm not going to do a rundown of every character in the film, but that said:
So, I'm going to start by saying a few things about Tom Cruise/Ethan Hunt - his age is really beginning to show, and so is his lack of acting range.
I'm not dissing on Cruise as an actor, but he's over sixty now, and it's clear that he's not the same spring chicken he was back in the 90s. I don't think this series has to end, but I don't know how long he can keep in the field - his fighting's a little clunkier, his running scenes (yes, they're still here) are a little slower. Also, while Ethan Hunt has never been a deep character by any means (heck, James Bond has more depth than him), the film really comes off as trying to turn him into, well, James Bond. For instance, in the scope of a single film, Ethan loses someone close to him prior to joining the IMF, Ilsa is killed (more on that later), and spends most of the film alongside a new character, Grace, while Alanna Mitsopolis (from Fallout) is still fawning over/flirting with him. It's not like there's been a lack of female characters in Ethan Hunt's life, but things feel very different here. The implied motif is that Ethan ultimately can't lead a normal life, and it's outright stated that anyone who gets close to him ultimately dies, or at least, is put in harm's way ipso facto. So when Ilsa is killed, clearly he's agrieved, but the acting is wooden in comparison to the emotion that should be felt at this point.
Kittridge is pretty decent. I'm not sure why he's been brought back now, of all films, especially since there's no explicit mention of the events of the first film, but whatever the case, he does his job well enough. Similarly, Gabriel functions decently as an antagonist, though "decent" is the key word here. He's stated to basically enjoy killing, not so much from the act itself, from the suffering it brings. So if the AI is a threat to humanity, then his allegiance to it kind of makes sense, but if so, it's an allegiance that really just boils down to "I'm evil." I know that MI has never really had deep villains, but even so...Also, he kind of approaches Gary Stuish territory, in that he can calculate events down to the second due to the AI helping him. For instance, he knows the exact moment to jump off a high-speed train, because a truck will be there at that exact spot at that exact point in time. Sure, okay.
Then there's Ilsa. Poor Ilsa, she's done dirty in this film. We can debate whether fridging is a thing (at the very least, I certainly agree it's a common trope in fiction, period, for Character A to die solely to serve the character development of Character B), but here's the problem - Ilsa's a pre-established character, and IMO, a very good one, and I know I'm not alone in that opinion. And there's a lot of things in the film that I do like with Ilsa, such as the gunfight she's in at the start, to her interactions with Ethan in Venice - little moments that aren't overtly romantic, but clear fodder for shippers, if you catch my drift. The problem, however, is that Ilsa is killed by Gabriel in the mid-point. Killed in such a way that it's less about the event itself, and more how it affects Ethan's character development, which is to say, not that much at all, relatively speaking. To be clear, I don't have a problem with Ilsa being killed, it's just that she's killed in a way that doesn't serve her own character, if you catch my drift.
Then that leaves us with Grace, who is kind of Ilsa's replacement. I say "kind of," because that's not literally true in-universe or in a plot sense, though Ilsa's death does mean that Grace has to do things that Ilsa might have been able to do herself. And given that she effectively joins the IMF immediately afterwards (more on that later on)...yeah. Thing is, I like Grace as a character. She's honestly fine, and thankfully, the film never pushes a romantic angle between her and Ethan. I like how the film is simultaniously able to show Grace as being extremely competent in her element (professional thief) and absolutely terrified when she's out of it (e.g. having to impersonate Alanna via face mask). I've seen some people claim that Haley Atwell is being pushed as a replacement for Tom Cruise, and while that's not too far-fetched a proposition (the IP is called "Mission: Impossible" after all, and Renner was originally planned as Cruise's replacement in Ghost Protocol), there's not really anything in the film itself that'll be the case. But while Grace may not come off as a replacement for Ethan, she DOES come off as a replacement for Ilsa, and I've already said how I feel about that.
Other characters to be sure - Benji and Luther are still fun, as is Alanna (she gets more screentime here than in Fallout, and it's highly enjoyable), but that leaves us with one more character to talk about, and that's the Entity. Yes, I'm evaluating the character of an AI, because that's how I roll.
The Entity (which I'm just going to call "the AI" from this point, as it's quicker) is interesting not so much that it's characterized, but the way it is. A lot of characterization it receives is exposited/inferred by characters, and while mostly that would violate the "show, don't tell" rule, here, it works. Among said characterization is that the AI is kinda implied to be like Ethan, in its penchant for going rogue. It's revealed that it was originally a US AI that was designed to perform infiltration 'missions,' but went rogue after being assigned to spook a Russian sub, instead destroying it, and merging with the sub's own network (hence why its core is a Russian sub now beneath the Arctic sea). The AI responds more aggressively the more people try to contain it, but otherwise, does its thing. But more directly, there's segments where the AI has a more immediate presence. For instance, in a night club, the AI is reflected by patterns of lights, forming something akin to an eye. I can't really do it justice, you'd have to see it, but the whole thing is creepy. Afterwards, it misleads Ethan through the streets of Venice by using voice clips from Benji and Luther, before using their own voices to mock them before they're forced to destroy their laptops.
To be clear, the AI isn't about to go down in pop culture history in the same way as, say, Skynet (even if its origins are similar in more ways than one), but credit where credit is due for making it a character at all.