As an American English speaker, I've only used "overlook" as a verb to mean "miss noticing entirely", but as a noun related to "examine", for instance a "forest overlook" might be a scenic turnout on the side of a road that provides a view where the forest could be "examined".
Similarly we use the word "oversee" for examining/observing... however "oversight" has taken on the role of an Auto-Antonym. We often use "oversight" and "lack of oversight" to mean the same thing, that something was missed due to carelessness... but we also use it to mean "supervision" that should prevent careless omissions from happening.
Similarly we use the word "oversee" for examining/observing... however "oversight" has taken on the role of an Auto-Antonym. We often use "oversight" and "lack of oversight" to mean the same thing, that something was missed due to carelessness... but we also use it to mean "supervision" that should prevent careless omissions from happening.