I sent my W an anniversary card, but that was a week before the bomb...she didn't give me one. I'm not sure what I'd have done if it had been after.
I think I agree with what you said. A quick call, just to say happy birthday, then maybe you just get off the phone cause you're really busy. Nothing wrong with acknowledging the bday in my view, and it isn't accompanied by any pressure. This is just you being a friend.
I also wouldn't bring up dinner, if she wants to she can bring it up. I say this cause you already suggested it and she was noncommittal, she knows the offer was out there and might have just been politely blowing you off. I don't know, I just think it sounds a lot like a date and might be too much pressure right now.
If you do really want to bring it up, I'd try to say it without any pressure at all: "So, I was trying to figure out my weekend plans and was wondering if you gave any more thought to the birthday dinner." Then if she sounds doubtful at all just say that's fine, maybe another time, or something. But I don't know, I haven't been pushing my W to do ANYTHING with me, so not sure what approach to use...
Me: 43 W: 41 Together 2009, Married 2011 Sons 10 and 6, Daughter 5 Bomb 2/21/21. W moved out 10/2021