[RPG] If you succeed on the saving throw for the Sickening Radiance spell, do you still gain a level of exhaustion and emit light

When reading the action block from left to right it follows this order:

1. Target one item. Creature, object, building, whatever they are looking for. Assume creature for this scenario.
2. Hit deals 2d8+6 piercing damage and 6d8 radiant damage.
3. Conditional if target was hit is a creature. DC 15 con save or die if they have 100 or fewer HP.

So they take the damage then make the constitution save. Proving it is a good idea not to make a Solar mad enough to attack you.

The "Opportunity Attacks" section of the PHB/basic rules states (emphasis mine):

You also don‘t provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction.

There is linguistic precedent in the rule that the word "move" does not expressly refer to the voluntary use of one's own Speed.

In the absence of specific wording to make sickening radiance an exception to the general ruling of nearly identically worded spells, the overwhelming likelihood is that it behaves like all the other spells described in the April 2016 Sage Advice rules answers column:

Does moonbeam deal damage when you cast it? What about when its effect moves onto a creature?

The answer to both questions is no. Here’s some elaboration on that answer.

Some spells and other game features create an area of effect that does something when a creature enters that area for the first time on a turn or when a creature starts its turn in that area. The turn you cast such a spell, you’re primarily setting up hurt for your foes on later turns. Moonbeam, for example, creates a beam of light that can damage a creature who enters the beam or who starts its turn in the beam.

[...]

Reading the description of any of those spells, you might wonder whether a creature is considered to be entering the spell’s area of effect if the area is created on the creature’s space. And if the area of effect can be moved—as the beam of moonbeam can—does moving it into a creature’s space count as the creature entering the area? Our design intent for such spells is this: a creature enters the area of effect when the creature passes into it. Creating the area of effect on the creature or moving it onto the creature doesn’t count. If the creature is still in the area at the start of its turn, it is subjected to the area’s effect.

Entering such an area of effect needn’t be voluntary, unless a spell says otherwise. You can, therefore, hurl a creature into the area with a spell like thunderwave. We consider that clever play, not an imbalance, so hurl away! Keep in mind, however, that a creature is subjected to such an area of effect only the first time it enters the area on a turn. You can’t move a creature in and out of it to damage it over and over again on the same turn.

In summary, a spell like moonbeam affects a creature when the creature passes into the spell’s area of effect and when the creature starts its turn there. You’re essentially creating a hazard on the battlefield.