There are hundreds of books, articles, courses, blogs, etc which address this question. There are also a large number of different, sometimes complementary, sometimes conflicting, answers.
The somewhat bizarre reason that I'm raising the question again now is a recent article in an established magazine about Philip Larkin, and something which, it is argued, impacted on his life and poetry. I found this on Twitter, and am not sure whether or not I'm glad I read it. I'm not giving a link, because you may not want to read it. (Except now you're really curious about it, aren't you?)
So, does a poem stand isolated from its author, or from its historical and cultural background? Do you just read a poem and see what it means for you/how it makes you feel, or do you do a close reading of the poem, based entirely on the text in front of you (and, of course, your knowledge of prosody, etc), or do you look at it in the context of what you can find out about the poet, their background, the time, place, etc when/where it was written. (I'm not going to list all the possible factors that could influence the poet and the poem - I'm sure you know what I mean.)
The question has been often raised about whether a poem should have explanatory notes, if for example, there are refs to Greek mythology, which not everyone may be familiar with, or whether it's up to the reader to make the effort to seek out that information, or whether the poem may well stand without that specific knowledge, or indeed, whether there should be references at all in a poem which the 'average' reader may not understand. No definitive answers on that question yet.
The question, based on the Philip Larkin article, could now become whether a poem should (also?) have explanatory notes that cover such biographical factors as may have affected the poem. Of course, in many cases, this information already exists with the better known poets - in introductions to collections, or in separate biographies, etc. Most poets, when a poem or collection is published, supply some biographical info, even if it's only where they live and where else they've been published. Reviews and blurbs often go into more detail about, for example, disability, sexuality, culture, class, etc, but not the detail given in this article, as far as I know.
So, to what extent, can or should, a poem stand alone? To what extent should the poem itself be able to convey its context, its intention? For example, I have mental health issues, which sometimes I want to explore in my writing, but sometimes it's just a background to my writing. Do I need to tell you that, or should whatever I write convey that, when it's relevant to do so? And when is it relevant? (Not here, for example.)
Which leads, of course, to the poet's intention. What does the poet want to convey, and how best to do that? What can the poet assume about the reader, if anything? How much can you put in one poem, or even a collection, to convey everything you want to convey? How much do you leave to the reader to work out, or find out? And what, if like Larkin, probably, you don't want the reader to know, or maybe you do, but not explicitly?
Do you judge a poem by the poet? What if, as has happened to me, you've read a poem, and you think, wow, that's brilliant (or some more literary response than that) and then you find out the poet is really not the great person you hoped they'd be (or worse). Yes, people you may not like can actually write poems that you do like. Except now you know what the poet's like, it's ruined the poem for you (probably an exaggeration). I'm not suggesting this article on Larkin would have that effect. Whether you like or dislike Larkin's poems or the man, such as you know anything about him from what you've read - and don't forget biographies (and autobiographies) are selective/subjective too - this new 'fact' is, at the very least, likely to prove a distraction when reading the poems. Is that a good thing?
You will gather I don't have the answers to these questions. I don't think anyone has. It's up to the individual, probably, to decide. But therein lies the difficulty - because people will often write or talk as if their view is right, rather than a suggestion, and also give you information that you didn't necessarily want (because it's impossible to completely block out this information - sorry). And, clearly, all of this can affect not just how you read a poem, but how you write one too.