Coming at this from the BS perspective, I think complete honesty is absolutely essential here, and that applies to both partners, regardless of who originally betrayed whom.
If the two of you have agreed to attempt reconciliation, then unless something has been explicitly stated otherwise, there is an understanding that you are both committed to an honest, open, and monogamous relationship. That doesn't mean he has forgiven you, that he has decided to stay, or even that he won't ultimately decide to leave. He has every right to make that decision, and unfortunately, there is nothing you can do to control it. But while he is participating in R, I believe he has an obligation to be honest about what he is doing and where he stands.
Muting the conversation and repeatedly deleting messages certainly raises questions. Speaking as someone whose reality was turned upside down by secrecy, I don't believe secrecy suddenly becomes acceptable because the person engaging in it was the one originally betrayed.
Your infidelity was your responsibility, and nothing he does now changes that. But his choices are still his responsibility. Being a BS doesn't give us a free pass to engage in behaviour that would otherwise violate the boundaries of our relationship. We can be deeply hurt, angry, confused, and uncertain about whether we want to stay, but those feelings don't eliminate our responsibility to act with integrity.
Personally, I wouldn't play detective or try to trap him. I would have an honest conversation about what you've seen, acknowledge your own insecurities and the damage you've caused, and ask him directly what this relationship means to him right now. He may be struggling with feelings he hasn't shared, or there may be a completely innocent explanation. Either way, you deserve an honest answer, just as he deserved honesty from you.
One thing I've learned through my own experience is that reconciliation cannot survive selective honesty. It has to apply equally, even when the circumstances and the responsibility for the original betrayal are vastly different. I too have had the urge to find solace with another since this began but I have not done so for the simple fact that I need to still live by my standards and honour.
Honesty is the best disinfectant. And if you're genuinely trying to rebuild something together, neither of you should be creating new secrets while trying to heal from the old ones.