what I think is irrelevant, what is relevant for a Catholic is what the Church teaches. A person in this situation is married, and therefore may not date or enter into any kind of romantic relationship unless and until the marrige is investigated by the canon law tribunal and a decree of nullity is issued. Part of that process will involve ascertaining if there is any hope of reconciliation, which until a civil divorce is obtained, is still hypothetically possible. The place to go for advice on this which will pertain to your own personal situation, not a general comment as given here, is to your own pastor. Prayers and best wishes for an outcome for you that keeps you in God’s good graces. As someone who deals with similar scenarios regularly as part of RCIA I strongly urge you not to enter into any new relationship on anything more than a casual friendship level until the matter of your marriage is resolved. To do so will lead only to heartache and the worst possible situation for a Catholic, separation from the Church and her sacraments.
The difference in what you have been told is likely based on the definition of adultery. If you define adultery as only involving sexual relations with a non-spouse while married, then a chaste relationship would not be adultery and dating would be acceptable. If you expand the definition to also include adultery of the heart (see Matt. 5:27-28), then becoming emotionally involved with another person while still married would be adultery, and thus dating would not be acceptable.
My understanding (thanks to this forum) is that all marriages are valid (not “assumed to be valid”, but actually valid) until they are proven otherwise. So even if you have the biggest “no brainer” in the world, you’re still validly married until the process is complete. It wouldn’t be acceptable to assume that an annulment will be granted and go out and date, you’d need to have the decree of nullity in hand before going out and acting like a single person.
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