I'm just going to start this by saying that this'll be my last response because I just think we both have different views on this and I think anymore discussion on the same topic is going to loop because of it. I'll chalk it up to a lot of the sticking points are things that
I personally don't need a lot of background reasoning to get behind for me to go "Yeah okay that seems fine." Mainly due to a personal enjoyment for old sci-fi schlock that usually doesn't explain anything (or has very poor logical explanations) so any sci-fi show I'm watching I give a lot more logical leeway. So I don't see a lot of the concerns you have as ruining the show, just feels like standard sci-fi to me.
Like:
Anti AI-Terrorist group without much backstory for existing
Doesn't go above the leeway because it's such a common group to have in Sci-Fi series (really any Anti-Alien/AI/Human/etc.) It being included in this series is perfectly fine, especially given what themes the show wants to explore. I don't need any kind of explanation for them to be there because of the need for the group in the series thematic storytelling.
Even the:
Mass of coincidences that allow a plot point to happen
Is fine because it's also super common in sci-fi series (especially when they're trying to quickly wrap up a movie and need a way to kill this unstoppable monster/alien). I felt that the backstory was interesting enough that I didn't mind it coming up. Same with the terrorists, it was used for the series' thematic storytelling around issues of AI.
I do agree somewhat with the:
I find it interesting that out of all the AI presented the most inhuman is Matsumoto who is supposed to be the most advanced. Vivy I think is handled pretty well on showing the awkwardness of AI when having the internal clash between their inherit mission and doing her appointed mission, but a lot of the side cast do fall into the pit of being too human. Show writers need to do a better job of showing the audience that a lot of the humanness of the AI is just good programming by showing situations where that "humanness" comes off as wrong. They did a good job of showing it during the peak into the AI uprising, but inside the story itself they haven't given enough to really show the AI evolving. They seem to want to show it with Vivy asking "What does putting your whole heart into something mean?" but I feel they should do more.
As for:
Vivy doesn't feel like she's developing much
I think they've been going really slow with this, but last episode left the writers a very good chance to do a strong development for Vivy
after having her seemingly stop functioning over the idea that her song had made someone kill themselves which goes directly against her one mission. I'm really interesting in this weeks episode due to this because I want to see what they'll do with Vivy. I think it'll be one of those things where you have to compare Vivy at the end of the series to her from the start to really see how she's changed.
I hope I answered all your points. I do agree that the show does have some problems, mostly with the characters outside of the main two, but the rest of it is enjoyable enough that I'd put it as serviceable. I just think it's better than your initial assessment that it wasn't worth watching.