Will it be distracting for the reader?
Firstly, I can't not comment on the following: there are immense amounts of telling in this piece. I feel that the sense of 'bad' writing being created here isn't actually formed by the action tags, rather the telling.
She bought it because it cost ¥499, and she loved prime numbers.
That specifically, and all of your other action tags are telling me things. Each one tells me information that could be shown in a more interesting way. It seems boring and bad because you're just telling me the information in such a plain form. I won't write for you, instead I'll give you the golden advice:
I'll actually give a very primitive example of what showing could be like for the above quote:
Aru beamed at the price tag: ¥499. A prime number.
It's obvious that she beams at the price tag because of the prime number. Rather than telling the reader that she loves prime numbers, you're showing them.
The Action Tags
To be entirely honest, I think you can leave them where they are in the sentence. However, perhaps you could add some indication as to how they are speaking. Here's a thought:
“It wasn’t suddenly,” Aru spluttered outwards through a sip of her Americano.
I think it would be good to do something like this because it helps more easily lead into the action tags. In your work it felt a little abrupt. It is almost as if something is going on, and then a fatal error has occurred and you have randomly decided to give me information. It doesn't flow, and I think this could help it flow more easily.
I hope this helped.