Use a better build solution (probably Vite)

[Inwerpsel]

The current Webpack setup was created based on the the WordPress plugin this library was originally embedded in, and never given much thought afterwards beyond just getting things to work. It's far from ideal: the setup is confusing and it builds slowly.

I guess Vite is the best option at the moment.

[Inwerpsel]

This is partially done, though it's not in a great state yet.

• I kept the CSS build inside of Webpack for now, to just focus on JS. It also has some trickier config (custom PostCSS plugin).
• I'm locally still using serve instead of Vite's server, because unlike Vite it allows to browse directories by default. This is very important for local development, at least for how things work now (that may change). Didn't find out the Vite config for that yet.
• Build for GitHub Pages still needs to be set up.