I think GP said "the datacenter" rather than "a datacenter" in the same way they would say they have a computer at "the office" and not at "an office". Even though there's no "massive office for the whole world".

Aren't you a native english speaker? At "the X" is a common idiom.

E.g. people say "you can buy carrots at the grocery store" despite there being multiple such stores.

"At the datacentre" doesn't imply one universal datacentre. It just informs you of which kind of facility you can use.

Isn't 'the' a definite article. You use it when you mean a single definite instance of something. If you mean something in general you use an indefinite article, like 'a'.

https://en.wikipedia.org/wiki/Article_(grammar)#Definite_art...

https://en.wikipedia.org/wiki/Article_(grammar)#Indefinite_a...

"you can buy carrots at a grocery store"

"you can buy carrots at the grocery store over there"

From the same page you've linked:

The definite article can also be used in English to indicate a specific class among other classes: The cabbage white butterfly lays its eggs on members of the Brassica genus.

And from other sources:

We also use the definite article:

to say something about all the things referred to by a noun: The wolf is not really a dangerous animal. (= Wolves are not really dangerous animals.) The kangaroo is found only in Australia. (= Kangaroos are found only in Australia.) The heart pumps blood around the body. (= Hearts pump blood around bodies.)

We use the definite article in this way to talk about musical instruments:

Joe plays the piano really well. She is learning the guitar.

to refer to a system or service: How long does it take on the train? I heard it on the radio. You should tell the police.