How does the Gloom Stalker ranger’s Dread Ambusher feature interact with Surprise?

In D&D 5e, if a Gloom Stalker Ranger uses their Dread Ambusher feature’s secondary attack on a creature during a surprise round (whether on the same target or a different one), is that creature still considered surprised?

This is important if the character is multiclassed with Assassin rogue, because Assassins auto-crit when hitting a surprised creature.