My suggestion: Don't do anything at this stage.
Your boss has already intervened, and decided to send the email. Let them figure it out - do not try to do anything now.
If you wanted to do something, you could have asked your boss at the time when they were expressing their dissatisfaction and announcing to send the email, that, you can try to check with the other team before direct escalation, as you had interaction with them previously. However, now once the discussion is over (and maybe your boss has already sent the email as we're discussing here), there is nothing you can or should do. If you try to intervene in a parallel communication, there are two risks:
- To your manager / team: You may come off as someone trying to belittle or stepping on the toes of your manager. They may not take this in a very good way.
- To the other team: You risk of being seen as someone who has created the trouble and now making an attempt to be in the good books trying to appear as friendly.
Take this as a learning, and next time, whether you are on the sender side or receiver side, insist on agreeing on exact dates for any requirement and delivery. The problem started with the fact that you did not have an agreed upon date for completion / delivery. Even if the timeline cannot be met (which is not very uncommon, specially in the software industry for example), the timeline will help to decided how much deviation is there and the amount of work still needed to get the target achieved.