In my opinion the answer is honestly pretty simple: blogs and RSS feeds. This was how it was done for years before social media came into the scene. You would find someone's blog, subscribe to their RSS feed, and anytime a new post came out it would pop up in your feed and you could read it. One important clarification is that when we say "blog" it can be pretty much whatever you want it to be. On my personal website I generally write more of my serious blogs, but on my bear blog I plan to be a bit more casual. It will be a place where I record short thoughts, ideas, musings, or cool things I find on the internet. Just sharing what I would normally share with my friends. That's what made the web great, and that's what I want to bring back.
I wish this was the world we lived in. Don't think it ever will be though.