Do you want to be in a situation where you're looking at receipts for the rest of your life?
I'm a WW and I did a TON of minimizing when I was in the middle of my affair fog. Saying words like "just XYZ", deleting messages and putting the blame of interactions on my AP. He sounds just like me.
1st, why is he deleting messages? Why isn't he coming to you and saying, "hey, I know this is going to hurt, but AP contacted me. I haven't spoken back to her, but I wanted you to know. I'm trying to gain your trust by being open."
Also, why has he not blocked her on all forms of social media/contact?? NC is huge for a reason- it's the only way you can even start to trust and stop reliving your horror from the affair.
Why is he picking up the phone when she calls? Why does he still care about her stupid dog? She's not his woman and it's not his business to be shoring her up in a difficult time. That's what family and girlfriends are for. This is a HUGE lesson I had to learn.
Your husband doesn't sound remorseful- he sounds just like me when I was thick in the fog of my A. Even if physical contact isn't ongoing, it sounds like he's still in an EA with this woman.
Do you want to continue to live like this? You can start the D process, serve him and slow walk it or stop if you see the progress you need. HOWEVER, you've got to be honest with yourself whether this is a partner you can stay married to- someone who doesn't put you first, doesn't own their shit and doesn't seem to want to work on it for his own sake as well as yours.
Do you want to be with someone who is uninterested in doing the work to help you feel safe enough to begin healing?