The Sword of Sharpness says:
When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target.
Do some other effects (language use is intentional) add on to this, or is it only the weapon's damage based on the weapon chart in the Player's Handbook?
Examples:
For the purposes of this answer I am only discussing the effect of the Sword of Sharpness that maximizes weapon damage dice. The effect of decapitation or additional damage otherwise in the weapon's properties are not part of this answer. Thus, if I say "Sword of Sharpness does not work on creatures" I am referring solely to its ability to maximize damage dice.
This is clear from the Sword of Sharpness description which states (emphasis mine):
When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target. [...]
Thus, any feature that only triggers when attacking a creature cannot even apply here. Sneak Attack is one such feature as gone over in the following:
The feature, for reference, states the following (emphasis mine):
[...] you can deal an extra 1d6 damage to one creature you hit [...]
Because Sneak Attack only works on creatures and Sword of Sharpness only works on objects, these cannot occur at the same time. (Probably)...
This, again, is clear from the description (emphasis mine):
When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target. [...]
Because of this, features that add damage to an attack that do not count as adding weapon damage dice have no interaction with a Sword of Sharpness. We have some questions related to this:
The first two are about features which explicitly apply to weapon damage dice (like the Sword of Sharpness) and the last one is a question about a feature that explicitly adds to your weapon damage dice. Most features do not explicitly add to your weapon damage dice and thus do not count as weapon damage dice and thus are not maximized by a Sword of Sharpness.
The Sage Advice Compendium states the following:
Q. If you use Great Weapon Fighting with a feature like Divine Smite or a spell like hex, do you get to reroll any 1 or 2 you roll for the extra damage?
A. The Great Weapon Fighting feature—which is shared by fighters and paladins—is meant to benefit only the damage roll of the weapon used with the feature. For example, if you use a greatsword with the feature, you can reroll any 1 or 2 you roll on the weapon’s 2d6. If you’re a paladin and use Divine Smite with the greatsword, Great Weapon Fighting doesn’t let you reroll a 1 or 2 that you roll for the damage of Divine Smite.
From this we can see that features like Divine Smite, which do add extra damage but do not explicitly add extra weapon damage do not count as weapon damage dice for the purposes of things like the Sword of Sharpness.
The Cavalier Fighter's Unwavering Mark feature is, as far as I'm aware, one of very few features which explicitly adds to your weapon damage dice. The Bugbear's Brute feature and the Barbarian's Brutal Critical are likely other examples. The three features mentioned use the following wording:
[...] The attack's weapon deals extra damage to the target equal to half your fighter level. [...]
A melee weapon deals one extra die of its damage when the bugbear hits with it (included in the attack).
Beginning at 9th level, you can roll one additional weapon damage die when determining the extra damage for a critical hit with a melee attack. [...]
Of course, Unwavering Mark only applies to creatures so it isn't affected by a Sword of Sharpness and even if it could apply to objects, if doesn't add a die of damage, but instead a flat modifier so it is already effectively "maximized".
The Sword of Sharpness only grants the maximum on the weapon damage dice, not on added damage dice. The weapon's damage dice are those dice explicitly tied to the weapon, not tied to any other applicable effects or features.
So a dagger's damage die is 1d4 and a longsword's (1-handed) is 1d8, and so on. According to this tweet from Jeremy Crawford, damage dice from magical weapons are also included in the weapon dice.
This answer on Great Weapon Fighting, a Fighter and Paladin fighting style, is related, and so I would extrapolate that logic to mean that the weapon's damage dice (on phb. 149) are maximized, not additional dice like sneak attack.
