I personally don't find Uta's issues to be appearing out of nowhere. They've been sufficiently foreshadowed imo. In addition to what you already mentioned, there was the event in the mall where Uta is visibly upset after Sensei leaves with Maki when he was originally there with her, Miku, and someone else (can't remember who rn) and she was in the middle of trying to get him to spend more time with them and go do something else. And then well before that event, when Sensei first gets her number, she mentions that her phone is incapable of sending pictures.
I think the reason that it may appear that her issues are surfacing all of a sudden is because of Sensei's approach towards her. Uta has been Uta-chan the cafe maid in his eyes since the beginning and he hasn't every really paid her character much mind besides his lascivious insistence on marrying her because of his love for maids. It's not until Sensei gets close to Io, whom he sees a lot of himself in, that Uta becomes more of an actual person in his eyes. Io also mentions to him that she (meaning Uta) got better and refused to really elaborate on that. And that was many updates ago. So all in all, there have been plenty of breadcrumbs dropped since she became part of the main cast that point towards there being something up with Uta and her past, but it's just never been much of a concern for Sensei until now, and so he never really monologued about Uta the person. It was always mostly just taking Uta chan at face value and not looking much deeper than that.
Good catch on Uta's reaction toward Maki during that evet, completely forgot about that!
(the name of the event is Food Groups btw. Revisiting the event made me realized that there was a close-up shot of Uta illustrating whatever insecurity she was experiencing, so it must meant something indeed)
I agree with the subtle clues here and there about Uta's issues, I guess what I thought was a hard segue is to connect her issues with these seemingly "normal" emotional reactions as a teenage girl who craves attention or affection (talking about her being upset by Maki or Niki showing up).
It could just be that Uta simply didn't want to act upon her own affinity toward Sensei for the genuine sake of everyone around, but still can't help feeling insecure when others act upon it; there isn't necessary for any of her issue to be involved during the process. We thought there could be issues involved because Io plain told us that Uta used to have certain issues, and these were the few occasions potentially applicable. While I have no doubt that there has to have issues involved, not knowing exactly what her issues are definitely isn't helping me connect the dots.
Perhaps, she considers moving closer toward Sensei (both emotionally and physically) counts as a type of impulsive behavior, an action that she must fight against due to the traumatic outcome in her youth by wearing another persona. But until future update gives more details on her issues, I guess I'll remain slightly confused. Perhaps I simply have become less patient and much more insatiable
like HOPE during the latest summer
However, I do like what you described there about how Sensei originally only saw Uta as Uta-chan and now more as Uta herself, hence explaining the lack of Sensei's deeper monologue toward Uta as herself and why all her issues seemingly surface only all at once now because of a shift in his focus at a different persona.
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Based on that, I also think it's possible that her issues sorta only emerge now because she has been pretty successful playing as Uta-chan in the old chapters up until now we enter Ch3. The other subtle clue I found is during Creatures of Habit, Uta stated "it's been a while since I've done any of the stuff old Uta was into", "And I've been feeling kinda...nostalgic lately...or something", "Like history is kind of repeating itself?" So Uta probably finds it harder to keep being Uta-chan and to keep old Uta at bay around Sensei, and thus harder to fight against acting upon her impulses. The reason why she feels like going back to her old self remains to be unknown; because of her feelings becoming more uncontainable? or because a certain god has stopped being dormant?