Medium is a good estimation of size (if you are equating it with creature sizes on a grid)
The game doesn't really list sizes in terms of dimensions of objects (beyond things like tables etc), and it is assumed that you would use the normal dimensions of such an object. So we need to work out whether or not this sword is an oversized sample, or a regular sized sample of this object type.
We can work the swords dimensionality from the damage of the sword in the stat block.
In the Dungeon Master's Guide there are rules for oversized weapons which state
Big monsters typically wield oversized weapons that deal extra damage on a hit. Double the weapon dice if the creature is Large, triple the weapon dice if it's Huge and quadruple the weapon dice if it's Gargantuan. For example, a Huge giant wielding an appropriately sized greataxe deals 3d12 slashing damage (plus it's Strength bonus), instead of the normal 1d12.
A creature has disadvantage on attack rolls with a weapon that is sized for a larger attacker. You can rule that a weapon sized for an attacker two or more sizes larger is too big for the creature to use at all.
The Solar is a Large creature, with a strength bonus of +8, and has this text in it's stat block:
Angelic Weapons. The solar's weapon attacks are magical. When the solar hits with any weapon, the weapon deals an extra 6d8 radiant damage (included in the attack).
In it's greatsword attack it has this text:
Hit: 22 (4d6 + 8) slashing damage plus 27 (6d8) radiant damage
A regular greatsword (from the PHB) deals
2d6 slashing + Strength bonus
So the damage dice of the greatsword are doubled in comparison to a greatsword sized for a medium creature (before the Solar's innate 6d8 radiant dice are included).
Taking all of this information together, we can see that the weapon is sized for a Large creature, and thus is a large greatsword, with damage output of 4d6 + Strength bonus, however a medium creature wielding this oversized greatsword will have disadvantage on all attacks with it (making the chance of critting with it significantly less likely).
But why does this matter?
In terms of how much space it controls on a grid, it's an object, and thus doesn't actually control any space on a grid, however it does take up space (since it's not an insubstantial thing). So an oversized sword should take up more space than a regular item.
Let's say, for ease at the table, we wanted to treat this object as if it were a creature (because reasons). Taking that into account, we do have an example from monster stat blocks on how big such a thing might be, it's called Flying Sword!
In the Flying Sword stat block, it is sized as a:
and is described as a magically animated flying sword (from which we should assume it's sized for a medium creature).
Thus, if we were to oversize the greatsword, this DM would expect it would be a medium construct if it were to be treated as an oversized Flying Sword monster.