Quick thing I wanted to jot down that I think would give strong context for Morgana's running away in Okumura's arc.
So for starters, one important thing to know about Morgana is that he's of a specific character archetype. He's a "pet," so he has no moral code meaning that you can't really expect anything out of him. Koromaru and Teddie are of that, and Teddie embraces it especially with how he behaves. One unique writing trope is that you can't really expect them to be "cool." I won't go in detail of how the two handle the trope, but basically Koromaru embraces it and only protects whenever necessary, while Teddie is an elaborate gut punch that builds up to something meaningful but forces you to double-down.
Exposition out of the way, Morgana's a character that seeks a moral code, or a "reason to live." At first he didn't have one and was willing to do whatever it took to achieve his goals: trick Ren and Ryuji, take the risk of afflicting a mental shutdown in Kamoshida, etc. Eventually Morgana would warm up to the Phantom Thieves, and it becomes a pretty prominent point past Futaba's arc during her recovery, when he becomes protective of her. You can tell Morgana's "changed."
But during their beach outing, Morgana ends up being referred to as "useless" by Ryuji, made fun of it even. That bothers Morgana: he tries to point out that Ryuji himself is unserious, but that doesn't make Morgana feel better. Rather, Morgana's upset about the idea that he's useless because it reminds him that it's not expected of him: that he can get away with it because he's a "pet." Ryuji can be criticized for exposing the Phantom Thieves for the millionth time but from Morgana, he can do whatever he wants and he'll be fine, and that bothers him.
That's the crux of the argument in September, Morgana wanted to prove he had a moral code, so he established unfitting standards on the Phantom Thieves that would clearly be detrimental under that context: they were about to act purely under the general public's desires, and the sudden influx of their fame unsettled them. It is later revealed that their fame was a trap set up by the conspiracy to frame them for murder. Under this context, what Morgana sought would completely destroy the Phantom Thieves. And again, remember that Morgana is "just a pet." He can "get away with it." And "that bothers him."
Morgana started an argument with Ryuji, accusing him of having become arrogant. Ryuji points out that Morgana is in it for himself too, but that is a reminder of Morgana's own origins: he doesn't have a purpose, and it's a reminder of just who Morgana is. So Morgana, holding himself back under his own standards, believing he doesn't belong, and he runs away because he wants to prove himself to the group.
That being said, Morgana did find purpose in the group, and that's his sense of justice. In Mementos, he decided he'd protect those he cared about, and that's the only sense of justice he needed. And rewind to Okumura's, the party encouraged him to let go of these superficial reasons and tell them how he truly feels.
That being said as a pet character Morgana has a similar style to Teddie. Not exactly a "gut punch" but leaning more towards a "what-if" than actively trying to manifest it. Like you're just left with this empty feeling after having faith in Morgana. And when you wonder about it, you try to see if it works, but it doesn't 100% "fit."
I think the pet archetype just consists of disappointments: you can call Koromaru one too, especially if you're introduced to him after all these well-rounded, intriguing characters, then he has an implied backstory, but as you try to look at him and see what makes him special, you just see a regular dog.
EDIT: I fixed the paragraph above, but I think that the mascots fulfill at least 1 of 2 roles: they leave you kinda left with just yourself after finding out your search is pointless, probably to make you realize that it's the search that mattered, something along the lines of "the real treasure was the friends we made along the way." Probably not, but the mascots exist to encourage you to find new depths in the mundane and think outside the box. No matter how many times you play, you'll see the pet characters and you'll be instantly lured to think about them having potential depth. Koromaru's for plot enthusiasts, Morgana's more user-friendly like "hey what could Morgana turn out to be?" And that way of thinking makes things interesting that the rest of the characters cannot do: they're like paintings, there is no incentive to look at them and understand them. But on second thought, yeah you'd be intrigued by the characters especially early on. And you don't need the pets' help for it.
TLDR Morgana is a disappointment by design and he doesn't like it. He's a pet to keep things interesting and keep you engaged.