I'll answer what I think are the underlying questions, clarified by 194 and Joachim in comments.
Antecedent Identification
The antecedent is the noun the pronoun represents in a sentence. When
you see a pronoun, you should be able to understand its meaning by
looking at the rest of the sentence. Look at the following sentence:
The Smiths picked apples for hours, and they put them in large boxes.
The antecedent for “they” is “the Smiths.” The antecedent for “them”
is “apples.”
... ... ... ... ...
As sentences become more complicated or whole paragraphs are involved,
identifying pronoun antecedents might also become more complicated [(and remember that an antecedent is not obligatorily placed before the pronoun)]. As
long as pronouns and antecedents are used properly, however, you
should be able to find the antecedent for each pronoun.
[Saylor.org]
And
Don’t allow too much space between the pronoun and its antecedent. If
you refer to Joe in the first sentence of a paragraph, and use him to
refer to Joe throughout that paragraph, and Joe is the only male in
that paragraph, there should be no problem. But if there are two males
in the paragraph, or if you’ve written several sentences since you
used Joe’s name, find a good place to use the noun again.
[Kathy Ide]
These guidelines are sound, echoing the Gricean maxim demanding clarity and ease of parsing (manner). Any prescriptive 'rule' barring antecedent-pronoun distribution across consecutive short paragraphs would be a broad-brush attempt to preserve clarity, and unnecessarily draconian in the simple extract in the question.
....................................................
How do you refer to a company in third person: it or they?
In English, both it and they are used to refer to a company....
The choice depends on many things: context, type of written
communication, house style, and more.
The common view is that in American English, company is referred to as
it, while in British English, company is referred to as it or they,
but they is more common.
In reality, many of those who write in American English use they to
refer to a company. And many people who use British English call a
company it. So there’s no drastic difference in usage on the two sides
of the Atlantic....
Whether you use it or they to refer to a company is a matter of style.
If you choose it, you can’t go wrong. But they sounds more natural in
many cases.
[Christina N; Language Editing]
If, throughout the [article], you refer to the company as a
disembodied corporate entity (more distant and impersonal), it/its ...
is probably preferred in your example.
Conversely, if you consistently refer to the individuals that comprise
the company, or its employees, or management team as knowable,
discrete, personable entities, they/their seems more natural to me.
Either would be considered grammatically correct.
[T R Gritzmann; Reddit]