The answer is no, there are no shields granting cover on its own and allowing to bash with them. Having such a shield would destroy the balance because tower shields would become obsolete in the face of a shield that does both and heavy shields would be at least challenged, depending on your playstyle. I am also not aware of any official publication that lists a scutum shield.
How to handle a scutum inside the rules
The scutum can be seen as heavy shield. It is lighter than a tower shield and does not provide full cover until you use a tactic like the testudo, that makes use of interlocking those shields and protecting a whole block of soldiers.
The scutum can be seen as a tower shield. It's almost the height of a soldier and should provide cover if used correctly. However, it was never actually intended to be used to bash in the way that D&D defines a shield bash. D&D defines a shield bash as an offensive maneuver in which the shield loses it's protective qualities and instead is used to hurt an enemy. The scene linked in the video is exactly the opposite. The roman soldier uses the full protective capacity of the shield against one enemy while striking for the other. The enemy the shield was used against took no "damage" in D&D terms. Using a shield this way is a very useful combat tactic and certainly shoves a more fragile warrior a few feet, but it is not giving up defense for additional damage. It's not a shield bash as D&D defines it and I doubt that the romans ever taught it to be used the D&D way.
Either way is fine, mechanically. You decide.
There are a few feats for fighters that go in that direction. Phalanx fighting for example. If you wanted to mimic Roman Legionnaires, you could house rule a feat for testudo formation fighting. I think it would fit right in with the other formation fighting feats. Rulewise the shield would be a heavy wooden shield and using testudo formation could grant cover instead of the bonus AC that other shield formation feats grant.