I understand why this is troubling to you. Your husband’s relationship with his friend is longer and maybe deeper in some ways than his relationship with you. Since you are sure there is nothing romantic going on between them, the friendship probably isn’t a threat to your marriage.
What is a threat to your marriage is your husband’s unwillingness to stop texting when the two of you are having personal time, like going out to dinner. That’s inappropriate at best. At worst, it indicates a kind of “addiction” to the texting rather than simply a habit of talking to his best friend. A habit can be compartmentalized. An addiction usually can’t be.
I suggest that you not challenge the existence of the relationship. Instead, ask him to consider how talking about everything all the time with his friend is preventing the two of you from sharing the experiences and memories that deepen a relationship. Reassure him that you think he can have both — a best friend and a wife — but there needs to be some boundaries around what he shares and when with each. There needs to be times when his attention is totally on you and his relationship with you, without a running commentary to his friend.
If the two of you can’t talk about this productively, I hope you will consider seeing a couples therapist for a few sessions. A therapist can provide a safe place to talk about difficult things and can offer some new perspectives that may help both you and your husband negotiate the situation with less stress.
I wish you well.