You are right, the point of the letter is entirely the candidate, any sentence(s) about yourself should be entirely to the point of facilitating communication about the candidate. I was told in school that all histories tell you as much about the culture that wrote them as the culture they describe, so you need to take both into account when you read them. I suppose this is true of reference letters as well. It's like introducing yourself before you ask an academic you don't know a question one-on-one over coffee at a conference – sometimes there's no need, but sometimes it's essential to framing the question & making the most of the other person's time & answer.
I have never been explicitly asked for a biography beyond "how do you know the candidate, for how long, and in what capacity". However, the UK is under a lot of legal pressure concerning letters of reference because some are so much better than others, not necessarily due to the candidate, but possibly due to how knowledgeable the writer is about writing letters. Possibly candidates deserve some credit for picking good letter writers, but this could be hard particularly for very junior candidates. So having guidance for writing a letter is useful, it's letting all letter writers know good practice by previous letter writers.
Personally I include biographical information (not a full biography) where I think it may be helpful and when I am trying to write a strong letter. Similarly, I also give information about our institution where I think it might not be known and be helpful. Examples: if I am writing a US institution from the UK, I let them know that I have attended US institutions & know what their programmes are like. Sometimes if I know someone well in the department I may point that out in the letter so that whoever is doing the search has the option of going to ask that person how seriously to take my opinion if they want to.
I put this at the end of the first paragraph or possibly as a stand-alone second paragraph, in advance of offering my verbose opinion of the candidate, so that the reader can have that information in mind when they see what my opinion is. The first sentence of the first paragraph says who the letter is for & for what position. The second sentence is my one-sentence summary of my recommendation. The third (or the second paragraph) is in what capacity I am writing the letter. That's where biographical details might be useful.