The answers are in (i) the Typescript documentation and (ii) the documentation of libraries that I'm using. I could get lucky with a Google search and it could be worth trying, but I wouldn't expect it to work. Personally my preference is to have a language and libraries with great documentation (Python, Java, Typescript isn't too bad [1]) and really know that documentation like the back of my hand.
If I hadn't had the LLM I would have probably figured it out the same way doing experiments, I might have asked my other "rubber duck"
https://mastodon.social/@UP8/113935901671533690
A tactic I didn't use, which helps in "legacy" systems where I am stuck, is start a fresh project in the IDE and try either reproducing the problem or building a tiny system which is problem free.
I'm hesitant to say what speedup I got out of the "figuring out the types together with the LLM" but emotionally I felt supported and in the process I wrote a whole lot, like I was keeping track of the process in a notebook. I feel a lot times when I have good LLM conversations I wind up writing better code than I would otherwise, not necessarily write it faster -- it's like pair programming.
[1] The typescript docs are great for the typescript stuff, MDN is good for Javascript and Javascript's stdlib
I have had cases in which a web search and some good old fashioned thinking have yielded better results than using an LLM, but on average I’m pretty sure the LLM has the edge.