First, please don't take this as a personal criticism, or that I'm saying that you do sound self-absorbed - we are in a comment section where people share their own experiences and opinions, so I don't think that expressing yourself in the first person is in any way negative.
However, to answer your question about how to appear less "self-involved", perhaps there's a structural trick you can use, which is to shift some of your writing from first-person to second-person and speak from the outside? How does this sound to you:
"It can take a while to learn that this can come across as self-absorbed and obnoxious in the US when speaking that way, so I've learned to consciously remember to ask questions about the person or the topic they presented, and void introducing related topics. This does make it more challenging to know when it's OK or how to actually switch topics (since, like the article mentions, conversations do flow from one topic to another) and this uncertainty can be anxiety-inducing"
I'm not saying it's essential, but as an exercise if you imaging talking about the situation that way, it can influence the tone.
I will repeat that I think your fear about sounding self-absorbed does not come out, to me, in your paragraph. I have worked with colleagues whose conversations do wander off on their own tangents if they're not asked to focus, and that may be similar to what you're talking about? But I can't be sure. If so, that is the difference between conversation for its own sake where sharing and opinion and life experiences are related, and workplace conversations which often have an objective, etc.