Noein: Mou Hitori no Kimi e is a lovely little show revolving around a group of children who have their world changed by invaders from a foreign dimension. The easiest parallel I can give you is that it's basically an anime cousin of Stranger Things.
The series focuses on the relationship between Haruka and Yuu. Both come from more or less broken families and have been friends since they met. Haruka is outgoing and friendly, while familial circumstances and social pressure has turned Yuu into a loner who wants nothing more than to grow up and leave town. Haruka is also a being called the Dragon Torque, which grants her certain (limited) reality-bending powers, that make her the target for a group of foreign invaders from the world of La'cryma - invaders that have surprisingly strong ties to them and their group of friends. Haruka forms a quick and deep connection with one of them called Karasu, who seems intent on protecting her.
Noein shines when it focuses on the kids and their reactions to the wild events of the story, as well as Haruka and Yuu's relationship with Karasu. Haruka struggles to connect with Yuu on a deeper level, and Yuu finds it hard to measure up to the fully grown and capable protector that is Karasu. The kids are all likeable and have relatable struggles with their connections to each-other and growing up.
The series starts to struggle a bit when it opens up the wold a bit more and showing you different vantage points of the whole story. While parts of them are interesting - that is, the parts that aren't complete pseudoscience gobbledegook - they take away from the heart of the series which is the children themselves. Similar to how a horror villain/monster often gets less scary the more is revealed about them, here the story gets more and more bogged down with uninteresting detail that isn't directly relevant to the children (as in, they don't need to know about quantum bullshit to progress the story) and takes more and more screen time away from the actual interesting parts of the story, which are mainly the relationships.
There are several adult characters that show up and explain the circumstances of the setting to the viewers, but they are rarely very interesting and their stories are often more than a bit disconnected from the core of the show. There's also a fair bit of politics about capitalism in the series that aren't exactly bad, but just feel like they come from a completely different show. There's even a sort-of Elon Musk stand in, who initially feels to cartoonish - until you realise it's a pretty accurate caricature of a childing billionaire who wants to the THE GUY without knowing his stuff. Ultimately he's such a tonal mismatch to the show that he feels wasted. The stakes that are attempted to be raised by the adult storyline doesn't really matter when positioned next to the central storyline and its events.
Speaking of adults, it's plain to see the effects that Haruka and Yuu's mothers have had on their lived. Yuu's father is abscent and Haruka's father lives in Tokyo so they both have single mothers. Yuu's mother is presented as the bad one, and she certainly is horrible. She wants him to study hard so he can go to a prestigious school in Tokyo, while struggling with her past and taking things out on Yuu, pressuring him to perform and isolating him from his friends. Haruka's mum is framed as the better parent, but this falters a bit when you shine a light on her behaviour. She basically locks herself away and works from home all day long. She sleeps in and doesn't take care of herself that well, to the point where Haruka has to cook and clean for her. In a way, it's not too bad for Haruka to develop some independence while young, but it's plain to see that being on her own without real limits and parental teaching has affected her emotional intelligence and she struggles to understand many of the relationships around her, and is reckless with her own personal freedom and self-sacrificing to a fault. It's especially evident how unreliable Haruka's parent is during one event where Haruka is missing and her friends are out searching for her together with their teacher. At no point during that event is Haruka's mother contacted to assist in the search or even be informed of her daughter's disappearance. The assumption lands at nobody really trusting her with auch responsibility.
Onto the aesthetic stuff: The voice acting is mostly very good, and has to do a lot of heavy lifting. Some performers are a bit miscast, such as the very recognisable Nakai Kazuya as Karasu who doesn't work very well with that part, imo. The music in the show in general is lovely and services the story well. The sweeping, orchestral score gives the exciting scenes way more of an impact. The art is generally pretty horrible, I'm sad to say. At times the barebones animation can work well, but the show is honestly quite ugly a lot of the time. Especially a few episodes in as the production quality takes an absolute nosedive.
All in all, I think it's certainly a show well worth watching, and one I recommend.