If using a scimitar*; slashing damage.
If using a short sword, rapier, dagger, bolt, dart, or arrow; piercing damage.
If using a sun blade; radiant damage.
The text is clear on what sneak attack represents: more lethal use of the weapon used in the attack.
... you know how to strike subtly and exploit a foe’s distraction.
If the attack is magical (due to the weapon being magical) the damage bypasses immunity / resistance to the damage type.
Vulnerabilities, Resistances, and Immunities
Particular creatures are even resistant or immune to damage from nonmagical attacks (a magical attack is an attack delivered by a spell, a magic item, or another magical source). (Basic Rules, p. 112)
A magical weapon is a magic item. That's how you get a magical attack with a weapon. The sun blade is a +2 magical weapon, so the attack is magical.
There isn't "magical damage" per se, beyond Force damage. There are magical attacks.
Damage types have no rules of their own, but other rules, such as
damage resistance, rely on the types. The damage types follow, with
examples to help a DM assign a damage type to a new effect. (edited
for brevity (Basic Rules, p. 75)) Acid. Bludgeoning. Cold. Fire. Force. Lightning. Necrotic. Piercing. Poison. Psychic. Radiant. Slashing. Thunder.
Magical isn't one of the listed damage types. Shortswords do piercing damage. (Weapons table, PHB, p. 48). Sun blades do radiant damage, and they provide magical attacks since they are magical swords. (Magic Item, see above).
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.
Note from the above: Sneak Attack's extra damage dice are bound to the weapon being used to inflict them. Many weapons cannot be used for a sneak attack, such as a quarter staff, a great club, a greataxe, a pike, a glaive, et cetera.
The amount of the extra damage increases as you gain levels in this class, as shown in the Sneak Attack column of the Rogue table.
From a practical standpoint, if the sneak attack did not do the weapon's damage type, there would be a serious nerf on the Rogue class since that is a major feature of their combat capability.
Sneak Attack and the Great Weapon Fighting fighting style have no relationship to each other. There are no weapons on the weapon table that are finesse that you can use for Great Weapon Fighting. (There is one magical weapon (rare) that is an exception to the rule: Sun Blade, which is has the finesse property. The rule on Specific Beats General (Basic Rules, p. 5) handles that lone exception well enough.
There is no contradiction; there is an exception. And here's the thing: GWF is a Fighter class feature. The tweet response was about a Fighter class feature, not a Rogue class feature. Sneak attack is a Rogue class feature. You are in the land of rulings, not rules, at this point if you are uncomfortable with this exception.
RAW supports the nova strike.
Great Weapon Fighting (Fighter and Paladin class feature)
When you roll a 1 or 2 on a damage die for an attack you make with a
melee weapon that you are wielding with two hands, you can reroll the
die and must use the new roll, even if the new roll is a 1 or a 2. The
weapon must have the two-handed or versatile property for you to gain
Sun blade fits all of this, so far.
Sneak Attack / Critical hit
... if you score a critical hit with a dagger, roll 2d4 for the
damage, rather than 1d4, and then add your relevant ability modifier.
If the attack involves other damage dice, such as from the rogue’s
Sneak Attack feature, you roll those dice twice as well.
you can deal an extra 1d6 damage to one creature you hit with an attack ...
GWF fighting style? Reroll damage dice. Crit? Added damage dice. Sneak Attack? Added damage dice. Reroll those Sneak Attack / Crit damage dice that come up 1 or 2.
So what do I do as a DM?
If this exception seems to you to be a problem, then the simple answer is "no sun blades in this world" or "no Rogue Fighter MC with that combo." Problem solved. (Tell the players up front, please). If, on the other hand, you are willing to now and again wallow in a Sneak-Attack-Sun-Blade-Radiant-Damage nova from the Thief/Fighter Multi class, then make that ruling and play on. (The Angels and other Celestials who resist radiant damage won't worry in any case ...)
As a side note, your question mixes apples and oranges. Divine smite has no relationship to Sneak Attack. Also, Divine Smite does radiant damage, not "magical" damage.
Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. The extra damage is 2d8 for a 1st‑level spell slot, plus 1d8 for each spell level higher than 1st ... (SRD p. 31-32)
Dev RAI commentary
I figured out all of the above by myself. Mr Crawford has offered his commentary.
Sneak Attack damage is meant to be of the type that's dealt by the
weapon, and it's subject to resistance.
1And again, the weapon dictates the damage type; Jeremy Crawford agrees.
Sneak Attack relies entirely on the weapon you're using. The weapon
sets the damage type of the extra damage, and the weapon determines
whether you can Sneak Attack at all; the weapon must be in the ranged
category or have the finesse property.
A further point about how weapon type is tied to sneak attack damage:
A magic item like the flame tongue and the frost brand deal extra
damage of a particular type when they hit. That extra damage doesn't
change the underlying damage type of the weapon. And it's the
weapon's damage type that is used by a feature like Sneak Attack