I agree about needing to let go of the compulsion of wanting to check his phone and I also agree to not be dismissive of this nor to minimize what it means in the scope of your marriage.
It takes some renewal of your bond to him. At the same time, going forward it's important for you to know there's some lines that cannot be crossed. They interact professionally in a way and there just cannot be any blurring of that.
It comes accross through your posts that there's a sense of you being in the wrong? Maybe I misunderstand? The interactions bother you. That needs to be respected. Trust can only be rebuilt with time, compassion and sensitivity. If he's toning it down, it will show and be clear overtime.
I'll repeat the letting go is of the compulsion to look at his phone not letting go and accepting their interactions as they have been.