Yeah surprised is more like a condition than anything else, it prevents you from taking any actions or moving on your first turn of combat or taking reactions before that first turn ends, but then it is removed and you can take reactions for the remainder of the first round when your turn is over.

Sage Advice clearing that up because it isn't very clear in the rules.

The other part that people seem to get wrong is if the individual is alerted to a singular threat that individual is not surprised, so say 3 enemies are laying in ambush for an adventuring party.

Enemy 1 Stealth check of 17

Enemy 2 Stealth check of 15

Enemy 3 Stealth check of 13

The passive perceptions of the party are as follows. Cleric 16, Rogue, 14, Fighter 12, and Wizard 10.

The cleric is not surprised because he noticed two of the enemies, the enemy with a 17 stealth will gain advantage on attacks against the cleric because he is not noticed but the cleric sees a threat and is not surprised.

It doesn't matter what the cleric does, he can call out "Ambush!!!" as load as he can this doesn't prevent any of his teammates from being surprised, the action is already happening and the ambush is sprung by this point.

The rogue is in the same situation as the cleric not surprised but two of the enemies gain advantage on their attacks against him.

The Fighter and Mage are surprised as they didn't notice any threat until it was to late, they don't get to take actions on their first turn or move, but as soon as their turn is over they are no longer surprised and could take reactions. This would be important for instance if one of the ambushers wants to run past the fighter, before his turn no attack of opportunity after his turn the fighter can make one, or if an enemy attacks the wizard before his turn the wizard can't respond with a shield spell, after his turn in initiative he can cast shield to stop an attack.