Yes, you can see normally in or through the darkness spell.
Devil's Sight says:
You can see normally in darkness, both magical and nonmagical, to a distance of 120 feet.
You have pointed out some confusion with the placement of the word "in" here. "In" is a preposition that connects "darkness" with something else in the sentence. In this case, it is connecting the predicate phrase "can see" with "darkness". We have "can see in darkness". Notably, the prepositional phrase "in darkness" is not modifying "you", it is modifying "can see".
"In darkness" indicates a modification to your ability to see. Your sight works when the thing you are trying to see is in darkness. It is not a requirement that you yourself be located in darkness. If this were how the feature was intended, it would instead read something like:
While you are in darkness, you can see normally."
When structured this way, the prepositional phrase "in darkness" is modifying "you". This is not how the feature is written, and so Devil's Sight allows you to see into or through darkness created by the darkness spell.