None of all these examples seem to be what the guide is talking about. I agree official communication and the website should be the company identity.
But the guide seems to talk about regular day-to-day communication on a startup. Jessica emails to a customer should have Jessica writing style in them, in my opinion. Just like any salesperson carries their own personality to a sales meeting.
Or internal emails between employees. You don’t write to Andrew to clarify some doubts about a report in the same tone of the company website. Or any standard tone. You write in your own style. At least I think you should.