I’m so sorry that he continues to cheat but won’t admit it.
IMO looking up ANYTHING about the OW and not telling you is a continued pattern of lying and cheating and disrespect and manipulative behavior.
I would also venture to say that he didn’t do it "just one time" but he just got caught "one time".
If he’s so addicted to the OW then sadly you are not reconciling. I’ve been in that place where I worked my butt off to R only to find out my H was still cheating.
I am going to suggest that you get a good counselor who is experienced in infidelity for yourself. It will be great to get good advice from someone who will support you.
Just remember this - liars lie and cheaters cheat and lie. If your spouse cannot or will not be completely honest now when your marriage is in the line, then I fear he will not change.
Unless you change, he may have no incentive to change. By that I mean that my H thought he could sweet talk me for a month or so and I would allow him to let his affair be swept under the rug.
When I did the hard 180 and told him I was filing for D, he STILL thought I would cave. He saw a side of me he wished he never saw. I took back all control and power in the relationship and he was completely blindsided.
Did he change? Yes he did. However it took years before I let my guard down. We are happily reconciled but only because I changed and thus, he was forced to change (of his own choosing).