The plots of Portal 2 singleplayer, co-op, and PTI are very “distant” from anything happening with Half-Life.

From what I understand (it’s been a while since I read up on the lore), Portal 1 and 2 take place after the Combine invasion of Earth, shortly after the first Half-Life game. That’s why Aperture Science is almost completely devoid of life, minus the personality cores that are attempting to continue running things. It’s because of the resonance cascade incident at Black Mesa that Aperture Science is now mostly defunct, and Chell is trapped as a lab rat at GLaDOS’ mercy.

So the Portal series is pretty reliant on Half-Life’s story to justify their plot, even if it’s never directly addressed in the game itself.