There's no certainties here. Only likelihoods. I'd say the likelihood is that he is still in contact with OW and waiting to see if you will 'fight' (or concede) to being in a marriage with him where he calls the shots (i.e. beginning with accepting his facts about the affair which you already know to be untrue). As to whether he is meeting her, we cannot know, but it's a very weird time and choice and fits with previous infidelitous behaviour. So that makes it possible. If he does do that we are just saying be prepared for a change in stance on his return that will seek to place blame on you, unfairly.
But perhaps asking you would be more helpful. Forgetting our suppositions, maybe there's a time for you to take stock of your own wants and needs when the time is right. You might wish to ignore these questions until you have spent more time building your strength and independence.
Why do you think he won't tell you the details of his affair and recent contact with the OW?
Why does he say he won't?
Is it important to you? is it necessary for you to move forward? Why? Are there any bottom lines involved in that? i.e if you discovered certain things that would be it?
What will you do if he doesn't tell you these things? Or continues to lie about them?
Have you asked him if he is still in contact with the OW and the nature of that relationship? Does it matter to you?
What has he done to make you believe he wants to make your marriage work?
Why do you want to make your marriage work? If you do.
What is your timeline now for being separate from him? Do you consider yourself single? Does he?