That's not even the point, though. Like you said, she's unlikely to be interacting with anyone outside Avalanche while wearing that, and they will either a) already know her or b) have been either introduced to her or briefed on who she is if coming from elsewhere.
No one who could benefit from the info actually needs it presented in that manner, so it's super silly.
The key word there is "unlikely" because Avalanche operatives are all plain clothes, and unlike undercover cops they aren't all carrying badges.
When you have a bunch of plain clothes members all together in one location, most of whom are unlikely to carry any sort of official signification, and also don't know one another, one member with that official signifier establishes a command hierarchy. That's important explicitly because it's going to be a common circumstance where not everyone will know each other. The purpose of her having that is because it places her in a position to be able to scrutinize anyone that she is suspicious of, but unlike just some other low level member who doesn't happen to know who she is, her official signifier means that it doesn't allow them the same level of skepticism back towards her.
Even in street gangs, the leadership have some sort of visual indicator on themselves, even when the lower members don't. This makes it easy for the smaller set of upper members to identify each other, and also easily make a distinction when someone copies that attire who they don't recognize, and check that out quickly within their inner leadership structure. This helps them avoid outsiders using social engineering to get themselves access to supplies or information, and helps keep out people from trying to spy on what they're doing.
Then that system actually reverses when you get higher up in the leadership, because then you have a visually verifiable and known smaller group of people who know all the people who they have to know. Then for everyone above that, they often lack any official signifiers in order to make it harder for external observers to be able to identify who's in charge, or pick out embedded senior members from regular nobodies. That means that the uniformed individuals stay extra vigilant about social engineering, and it helps keep particular cells at whatever level of awareness is best for what they're being used for.
For her, all about the simplification of a passive hierarchy that allows her to operate from a senior position of authority, and also makes it easier to ensure that there aren't plain clothes outsiders just pretending to be important members from another cell that can fake their way in.
Also, she probably wears it all the time, because costume changes in videogames take lots of work compared to just putting on a jacket in real life.
EDIT:
I just saw the character descriptions, I felt like it was worth mentioning that Yuffie's character bio describes her as a "Shinobi"《シノビ》with the word spelled out in katakana & in quotes, rather than just using the literal term for ninja/shinobi (忍者). That's an interesting bit of nuance, since during the victory scene in the trailer, Sonon says the equivalent of,
"That's how ninjas do it." in both languages, so there's probably some nuance around Yuffie as a "ninja" potentially being something of a self-designated title rather than an official field of study that she received from a master, like how Tifa studied under Zangan & Sonon studied under Yuffie's father Godo. That helps to communicate the sort of tone where he's definitely not being patronizing towards her for it. Especially since Yuffie's ninja obsession was always supposed to be somewhat in defiance of her dad, I think that there's likely something being set up there.
Also, I've always found it interesting that in the original game, the only person who appears in ACTUAL ninja attire is the person that Don Corneo uses to kidnap her, so I'm wondering if the distinction in the katakana there is also so that they can use the real term later on. That might be why they use "Ninja" to refer to Yuffie in English despite how it's written, so that they can keep the term "Shinobi" for later in the more literal sense of trained assassins, since the term "Shinobi" carries more weight in English, and can still manage to carry that connection.
Lastly, this bit: "暴走しがちな先輩を優しくフォローする。" mentions that he gently follows his senpai who has a tendency to run away, which provides a fun bit of context to his introduction scene at the Avalanche cell.
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