If you are still married, you ought not to date.
This is an integrity issue. A vow is made to “forsake all others” and dating another while that vow is in effect legally is a violation of your word.
Cheaters do this all the time. They make up “excuses” for why they are “allowed” to do this.
Don’t be like them.
Maybe your Cheater informed you that they had decided your marriage was already over, and that is why they could go on “dates?” This was probably new information for you. It sucks.
This is why–in part–why I did not date while my marriage was in limbo between divorce filing and actual divorce granted. Plus, those energies are best spent on rebuilding self-worth among other self investments.