Like what we have in Heroes / Dota 2.

We don't have this feature yet. We're in the early design stages of what exactly match history can/should be for OW right now.

Overwatch now features a replay tool that shows your most recently played matches. However there still is no match history function for past games. It was revealed recently in 2020 that this is still on their project radar, but it may be not until Overwatch 2 comes out before we finally have such a feature.