It seems silly not to do ‘lunch with a friend’ any other day.
But they are not platonic friends, @Lala727. They are affair partners. I’m so glad that @bleughgreen has provided the link re Not Just Friends by Dr. Shirley Glass. Please read this to gain clarity about the shifted dynamic in your relationship.
Respectfully, you are still under-reacting to the blatant affair that your P is conducting in plain sight. His primary emotional relationship is now with this OW, so he was never going to cancel his Birthday date with her. After a year or longer, they are heavily invested — hence the constant contact, reaching out on holiday, bringing in the New Year together, and having a birthday meal. I imagine there have been other meet-ups, lunches, etc.
I just saw your update about your brother noticing early on how ‘glowy-eyed’ P is with OW, and also how he sits with her in your presence. Added to the current intensity of their relationship, those two examples speak volumes. He has been making a mockery of you for years. Any ‘reassurance’ he has given that she is a platonic friend is pure manipulation and gaslighting, as his obsession/emotional reliance on her is utterly obvious.
In your shoes, I would tell him definitively that their intense relationship crosses your boundaries and is inappropriate. It’s emotional infidelity, at the least. Tell him you are not interested in continuing this relationship where another woman and their connection is his focus and priority.
If he doesn’t cut her off, I’d be done with him.