I second the "friend" comments above. I've moved to being cordial and pleasant but I'm not communicating anything more than logistics. I agree with you that it's tough - we have a level of intimacy and shared background that makes conversing easy. As soon as the D is finalized, though, I expect these to be few and far between. My W had said that she wanted me to come to her family's home for holidays, etc. Nope. Haven't said that yet but will politely decline all joint activities going forward.
At a higher level, I'm not proactively informing her of D3's activities (e.g. if she wants to know that D3 had a bath last night she can ask me, I'm not telling her). I do inform her when I will be taking D3 out of town but it's this: "FYI, I'm taking D3 to [hometown] this weekend, she'll be there Fri-Mon". I'm not even acknowledging TMs from her that I don't need to (FYIs, etc.).
All that to say that you should make this as easy on yourself as possible - if in doubt, don't communicate it out. Unless it's something your W needs to know for logistics then don't send it. Keep all messages brief. Don't tack on any personal stuff. Don't even put in small talk ("House is locked up. Crazy weather, huh?"). If you want to communicate with someone, do it with other friends, coworkers, or at your new hobby (you're getting those, right?).
M(35), W(35), D(4) M-9, T-12 Bomb Drop (D announcement) - May 3, 2019 W moved out Aug 13 House sold Sept 25 Papers signed Nov 15 Divorce finalized Dec 12