Another example of sentence-initial so as a discourse marker (and also, not an “annoying” kind), is this one:
(4) So, how have you been?
Notice how it doesn’t show that the sentence following the so is caused by something that came earlier, and in fact, it could be the first thing spoken to someone who just entered the room. Or, it could be a way of changing the subject, mid-conversation. That shows us more about why the so is called a discourse marker: It’s something a speaker can use in conversation to refer to information that both speakers have. In this example sentence, we would need context to know what the so is being used for.
Discourse markers connect ideas together in a conversational way.
Now we know that discourse markers connect ideas together in a conversational way, and that usually, the listener understands what the speaker means by knowing the context of the conversation. Other discourse markers are words like well, still, anyway, and besides—mostly when they come at the beginning of a sentence. They can be conjunctions, adverbs, and prepositional phrases, and they serve to express various sentiments to the listener, without actually contributing anything grammatical to the sentence (4). If discourse markers are left out, the speaker might sound a little less natural, but the sentence would still make sense. Here’s an example, with discourse marker well:
(5) A: How are you, Jill?
B: Well, Jack, I’ve been a little sick.
By starting with well, Jill is trying to form a personal connection to Jack and maybe even trying to show that she understands that he is likely expecting a positive update. The well can serve to signal that Jill is delivering unexpected news. The specific meaning depends on the context of the conversation.
Getting back to discourse-marker so, another way people use it is to find out if earlier information has been understood correctly, like this:
(6) So too much vitamin A can actually be harmful?
Yet another use is to summarize information mentioned earlier in the discourse, like this:
(7) So that’s how the game is played.
[Note: You could put a comma after so in the last two examples, but it is optional.]
A final example of this non-exhaustive list is one that linguist Galina Bolden has pointed out: We can use so to return to a topic that was brought up earlier in the discourse, from which speakers got distracted, like this:
(8) Jill: I got a job interview today! Oh, and my cousin is visiting next week. She’s really excited.
Jack: So tell me about the interview.
As you can see, discourse markers serve a wide array of purposes, which speakers use and understand without even thinking about it.