Just some opinions...
One, is it really mutually exclusive? You can always ask the LLM to explain step by step how something works, even as it gives you sample code. They're great for learning too. One time I had some analytics with a few tens of thousands of data points and the lookups were getting really slow, so I asked ChatGPT to explain how to make it faster and it taught me basic binary trees and how to use them (I never had a formal CS background, so didn't know anything about data structures and such). I found its explanation to be much clearer than most of the human-written articles I found online. But the code also had some minor bugs that I had to clean up. It got the gist of it, though, which is further than I'd have gotten on my own.
Two, does it really matter? Are you a generic web dev (no offense meant; I am one myself)? If so, most of the time we're just converting generic business requirements into generic web pages. It's the sort of thing that people do 10,000 times a day, using the same basic patterns. It's the sort of thing that LLMs will be able to easily do themselves in a few years. They're much faster learners and much more able to keep up with the latest trends and standards. But right now, they're still relatively our peers, able to share knowledge and feedback the way a coworker might, but also can make mistakes the same way a coworker could. I never once asked myself "what's worth learning on my own and what should be punted to a LLM". When faced with a business requirement, I research everywhere I can: my own experiences, LLMs, Stack, NPM, my coworkers... and working together, humans and robots both, the team usually ends up with some sort of workable solution. It doesn't have to be perfect, since it'll be obsolete and rewritten in a few years anyway.
On the other hand, if you're not just a boring web dev and want to specialize into actual algorithms and comp sci stuff -- becoming the next John Carmack, say, and actually solving novel problems -- then, sure, having a solid understanding of things would be helpful. You'd get to provide the training data for the next generation of LLMs while the rest of us just consume their (and your) findings.
So it really just depends. If you want to learn for the sake of knowledge, do so. If you just need to get a workable component made, nobody cares whether you wrote it yourself, you used a library, or you got help from a coworker or LLM. Web dev is just the plumbing of the internet, and reusing code saves everyone time. If it frees your time to do more UX or testing or bugfixes or features, that's a win-win.
For what it's worth, I find high-specificity queries (like "given a data object like ____, how do I make it ________") to be more helpful than broad "make me a component that does X" type queries. I also stopped using Copilot because it wasn't very good compared to ChatGPT. When I did use it, though, its advice got dramatically better when I provided thorough comments, which have the side effect of helping other human devs too.