I've been working as a bona fide junior developer for almost 6 months now and I've got a reasonably good handle on the foundations of web dev stuff...
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The HTML
<template>element. A lot of people just default to using complex application frameworks like React or Angular even for stuff they really don't need to just so they can get the templating functionality they provide. In reality though, if all you need is basic templating, you can get it easily by just using HTML<template>'s yourself, and it will often outperform the templating provided by many of those frameworks.IndexDB, Web Workers, WASM
How far do you need to know WASM if you are using JavaScript?
WASM is about creating bindings between one language, like Rust, and JavaScript. So if I have a function that does expensive calculations I could create it in a faster language like Rust, create a binding for it and compile it into a wasm module that gets imported into JavaScript. Then I just use the function as any other JavaScript function. So to answer your question, you don’t need to know wasm at all, you need to know a compiled language and the simple API that provides the bindings.
I’d suggest exposing yourself to new ways to think about problem spaces, rather than spending time diving into specific technologies if you don’t use them on a daily basis. The return on your investment will be higher early on in your growth as an engineer.
Some examples from my own life:
RxJS Observables - they're like Promises on steroids. But so that you don't have to climb their steep learning curve, I've written a helper library called polyrhythm that gives you a feel for what they can do in a friendlier coding style. :)
Here's a chat app that works like the one on your phone: codesandbox.io/s/poly-chat-imw2z
I'll be making a dev.to post about that soon, so I'd appreciate a follow if you're interested!
Things like Observables and programming patterns would also be helpful to know.