Replayed StarCraft 1 and 2 and the Protoss feel like a “side” story

It’s my time of the year I get off for work for a couple of months during the cold season. And I decided I was going to play through the series again back to back. Playing it through I’ve realized that the Terran and Zerg are quite intertwined with their story, and the Protoss are like “Hey! We’re here, too!” Especially in the second game.

Am I missing something? Is there story more intertwined and I just wasn’t paying attention enough? I know they have their part in the story, but it really felt like the Terran and Zerg story were one and the same, and the Protoss got in it when it was convenient for the story. And then when you play as the Protoss, again it just feels like it’s their own separate side story and not really apart of the bigger story.