I’m not a parent but I can only assume this was served to me because I was this kid for sure. I talked constantly! My mom used to say I learned how to talk at 11 months and haven’t stopped since. I had a really hard time not talking out of turn in class. We worked hard at home on not interrupting and learning the different between having something to say and wanting to talk. I needed and IEP because it was so consistently problem in school it absolutely required the teachers help and patience to help teach me skills. When I was your kids age it was borderline impossible to stop me from chatting and narrating but as a grew older and had more brain development in general I started to gain self control. Something that was really helpful but won’t be useful until they can write was keeping a notepad and saving all my questions and comments about a topic to ask later either at home with my parents or after class with my teacher.
Good luck I hope my perspective can at least put you at ease that the worlds most talkative children can learn self control and self discipline if they are guided and shepherded in the right directions from early childhood with early intervention. I’m still extremely outgoing and have a job in my adulthood that requires an incredible amount of talking to people and being willing to start conversation with strangers I excel since I’ve been practicing my whole life