Since you asked for a reputable source, I am going to begin in this answer with a reputable source and then move on to the specifics.
What you are asking about is the usage of the definite article "the" alongside noun phrases (NP) structured around the preposition "of". "A of B" is an interesting structure, because you have a noun, the head of the NP, followed by a prepositional phrase. Therefore, syntactically the structure of the phrase is:
A [of B]
use [of sanitizers] (non-count of count plural)
a page [of a book] (indefinite count singular of count singular)
the branch [of a tree] (definite count singular of count singular)
the eyes [of the man] (definite count plural of definite count singular)
where A is the head of the NP and determines the definiteness and grammatical number of the NP.
Count Singular NPs
Huddleston and Pullum in The Cambridge Grammar of the English Language (CGEL) (Huddleston & Pullum 2002) differentiate between count singular NPs and plural/non-count NPs with the definite article. Their analysis is pretty concise and undeveloped and this usage is sort of glossed in passing. I am going to give an outline here. On page 369, Huddleston and Pullum suggest that when a count singular NP takes the definite article, identifiability and uniqueness are key.
There are a couple cases associated with this usage. It could be that the speaker recognizes there is only one entity relevant to the conversation, which is the specificity you mentioned in your question. Also it could be that there is no need to identify the specific A. This comes a bit counter-intuitive, as it almost looks as the opposite of the specificity principle, but in context it makes sense.
Why don't you put the key in the pocket of my jacket?
He married the daughter of his bank manager.
There is possibly more than one pocket on the jacket, but in asking that "you put the key in the pocket of my jacket", the speaker implies that in their mind there is no need to identify which pocket they would like to key to go into. And the speaker doesn't really expect the other party to ask "Which one?" because the speaker expects the listener to understand from the use of the definite article and a singular count noun that any one would do is implied in the sentence. Similarly, the bank manager may have more than one daughter, but there is only one relevant in the context. Maybe other daughters are unknown to the listener, or already married. This hinges on the speaker's perspective and expectation. (I agree with LawrenceC on this part.)
Plural and non-count NPs
This part concerns your question at issue more than the first part does. Huddleston and Pullum group these two together and give the explanation that use of the definition article together with plural or non-count NPs is indicative of totality. This section in the book is really short and not really well-explained, but here is the idea in my own words. When you say:
I hate the residents of that tall building.
You are saying you hate all of them. You are taking all the people living in that building as a whole, as a collective unity, and you hate that collective unity. It doesn't matter if someone has just moved in yesterday, you still hate them. Probably because you want to buy the land that building is sitting on and anyone living there is in your way. So you hate them all. But if you say:
I hate residents of that tall building.
There is much less of an assertion that "everybody in that building is hated". You are instead saying you hate some, maybe most, people living in that building for some reason. It could also be everyone in the building that you hate, but without the definite article you are not making that strong of a statement. Maybe you live close by and you are annoyed by the constant noise coming from that building. You don't know who causes the noise. You only know it is from that building. So it's very likely that only a small number of people are responsible for the noise-making.
The same goes for non-count NPs. I am going to explain this part in detail later using your sentence and some other sentences as examples.
It is important to note that when someone uses the definite article "the" they presuppose the existence of the entity and the other party is expected to identify the entity because it is assumed to exist in the first place. This is very relevant to your sentence.
Now let's look at cases of non-count NPs and specifically the sentence at issue.
He mocked the use of sanitizers during the pandemic.
The inclusion of the definite article makes the NP definite and thus presupposes the existence of "the use of sanitizers". Namely, when you say this, you are saying you know for sure sanitizers are or have been used during the pandemic. Does the adverbial "during the pandemic" make it more likely that the definite article "the" is used? Maybe. The key here is totality, remember? When you specify a time period (temporal qualification) or a location (spatial qualification), you are making the total entity being referred to more identifiable. But still, it is perfectly fine to say "He mocked the use of sanitizers." if you are talking about the act of using sanitizers, like every time that someone uses a sanitizer is counted.
When you say
He mocked use of sanitizers during the pandemic.
You are not presupposing that this phenomenon indeed exists. This sentence lean (slightly) denotatively towards that it may or may not be the case that people are using sanitizers during the pandemic. It is less strong, less assertive. Also you are not taking it as a collective unity. You are talking instead about an specified number of instances where stanitizers are used. You could be commenting on his behavior towards some instances of sanitizer use.
This point may be better driven home with some other examples with nominalized verbs in the same construction (all of the examples are from native speakers):
Miki sought to compromise by agreeing to inclusion of an anti-hegemony clause with wording that would hopefully soften its anti-Soviet connotation. (source)
If the negotiating process leads to inclusion of an early-termination option, it must prohibit the sponsor from arbitrarily or suddenly terminating the agreement or decreasing pledged funding prior to the expected term (source: American Association of University Professors)
These two examples are sentences sans article where inclusion is talked about as an not-yet-certain and less-than-definite matter.
Thanks for being such an exemplar of mentoring, the inclusion of diversity, impactful scholarly writing, and generosity, not just for us, but, for our field.
In this sentence "the inclusion of diversity" has already happened and is being taken as a concrete example in acknowledgement.
Some clinicians make greater efforts than others to encourage generalization of socially skilled behaviors outside of the therapeutic context. (source)
This is another article-less example that talks about "generalization of socially skilled behaviors" as a general concept. The speaker could have some instances of it happening in mind when speaking, or none at all. The point is that there is no totality to speak of in this sentence.
You should also note that the nuances and shades of meaning are there depending on whether the definite article is used or not, but not everybody follows this in actual speech. That's why as FumbleFingers has explained it could be subjective. This answer points you to likelihood. That is to say, in some contexts when the conditions that I have explained are met, it is more likely that people will use the definite article. But still it is not an ironclad rule. For example, even if I am talking about all the residents in a building, I might still say "I hate residents of that building." But tomorrow I might include the definite article when I talk about the same matter again.
Btw, I agree with Lambie that "usage" sounds foreign (non-native). I think the reason you see usage a lot these days is probably due to the influence of it being used in the IT and other high tech industries (cf. CPU usage, RAM usage) and that a lot of non-native speakers working in these industries use this word.