How do you manage multiple lines of inquiry as a curious person?

Don't focus on the 'intended material' (unless you have some responsibility for it), follow the "lines of inquiry". Trust your instinct: You will learn better the things you have a passion to learn, will enjoy, and are ready for - that are not a step too far; your instinct guides you toward where you are ready to build next.

And I think people learn better by inductive, exploratory learning than by some predefined path (and I've read things that support my theory, but I can't say I've looked for or seen any great evidence). Trusting my instinct has made all the difference for me.

I do have to prioritize, of course - there isn't time to follow every path. I'd like to learn just about anything in the universe. But at the same time, when I choose something, I follow it (almost) as if there is no time limit.

Open a new browser window before you venture into the new topic. That prevents all those tabs from getting mixed in with your more essential work (gmail, calendar, jira, Trello or whatever). Open a new window again if you feel like you've branched off into a different topic.

Then periodically, or when you're done, review the tabs, close most and save the good ones away with a brief note. BrainTool[0] is an extension designed to be exactly a 'topic manager'. It's a combination tabs and bookmark manager that captures notes and writes out to plain text. Might be the tool you are looking for (disclaimer, I wrote it!)

https://braintool.org

I use Sidebery. It's a tree-style-tab manager. Of course, it doesn't help with stopping rabbit holes, but it allows me to return later and see my "path of exploration" - which tabs correspond to which subtopics.

Another thing I do, which can help with stopping rabbit holes, is to take notes. Even just an ephemeral document. It helps with future memory call, you can use it if you need to jog your memory later, and most importantly you'll get tired of taking notes at some point. That should push you to get "back on topic".

I'm not sure rabbit holes are all that bad though, because some of my best ideas have resulted from following them. It's good in moderation.

"It is a painful thing to say to oneself: by choosing one road I am turning my back on a thousand others. Everything is interesting; everything might be useful; everything attracts and charms a noble mind; but death is before us; mind and matter make their demands; willy-nilly we must submit and rest content as to things that time and wisdom deny us, with a glance of sympathy which is another act of our homage to the truth." - Antonin Sertillanges

If you are not looking for answers, you're looking for questions. And if you can't find questions, your are browsing aimlessly.

If you are just following unspecific hunches, try working within a workflow where this information you piece together converges to something more specific. The Zettelkalsten fad has one key good point, and that is, if you process your notes in a particular way, you can let the knowledge itself lead you to where you want to go over time. However, this does involve taking the time to process your information to a degree before it works.

Finally, if you are not taking the time to process the information before you, you are not learning things, but merely learning about things. How to make the transition from "learning-about" to "learning"? If you're not looking for answers, you're looking for questions...