No the Long Sword is a bastardization of a Greatsword hilt and a long sword blade. Longswords and Bastardswords are more or less the same thing. The monstrosity Larian has made is neither. I'm going by the currently used names. The names of swords have changed all through history, usually comparing one blade at the time to another blade at the time.
I don't know where you get the impression that the BG3 longsword uses a greatsword hilt. The longsword was primarily a two-handed weapon and the hilt was designed to accommodate this. The greatsword (an Early Modern/Renaissance weapon, but hey, so is the rapier) generally had a grip forward of the cross-guard because greatsword fighting styles often required gripping the sword there.
I don't know what you are referring to as 'currently used', whether that is the terminology used by antiquarians and historians, or the term used in RPGs, but I suspect the latter. 'Longsword' to a medievalist or anyone academically involved in history is not a one-handed weapon (that's an arming sword). As a pseudo-medieval setting, a longsword in the Forgotten Realms should look like the one on BG3. Maybe slightly shorter, but not by a huge amount (inches rather than feet).
The 'bastard sword' was actually applied to a sword between the longsword and the arming sword (hence the name).
You're right that names vary, but the medieval 'longsword' nomenclature is pretty well established. Or we could just use Oakeshott's 1960 classifications and sword names could become a spaghetti of Roman numerals.
