The prefix de- had more than one meaning in Latin, and many of them persisted and developed over time. Like all core morphemes, the meaning is extremely hard to define and pin down the semantic nuances. At least we’re only dealing with the bound morpheme here, not the free one, which has a 22,000-word definition! (Interesting how dictionaries went from defining rare words, which are easy, to common words, which are impossible…)

Here’s the Wiktionnaire article on what de- could mean in Latin.

1. marque un mouvement de séparation, d’éloignement : decidere, etc.
2. renforce le sens du verbe, marque l’achèvement, la plénitude ou l’intensité : declamare, etc.
3. sens contraire, marque le manque ou la cessation : deformare, etc.
4. Il peut y avoir contraction : dego < de ago, etc.

Since our base morpheme is gradus "step, stage, rank, position" it would seem that degree is likely formed on the second definition, reinforcement, rather than on the first or third as Etymonline supposes. However, as hinted above, there are definitely more than just these four meanings of de- and perhaps another shade more closely aligns with their explanation. Either way, we are not limited to "the lack, cessation, reversal, undoing" sense.

Many other words are formed on similar senses of de-, including définir lit. "to set a finis, boundary"; délimiter in the same meaning; déclamer lit. "to cry out"; and so on. Look and you’ll find that undoing is not the only sense.

We should observe that words can be derived multiple times throughout history from the same roots in different senses, ending up phonologically the same but semantically different. Hence "degrade" and "degree" have the same elements, but are not derived from each other; they were based on different senses of de-. Compare English be-, which can mean either "provisioned with" as in "befeathered", or "to remove" as in "beheaded". Either of those could easily have had the opposite meaning of the one they have.