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KaTeX does not support all LaTeX features but initializes very quickly.

LaTeX via WebAssembly supports more features but might need longer to initialize.

There's an existing WebAssembly project: https://www.swiftlatex.com

There is TikZJax[1], which apparently compiles TeX to WebAssembly, to run TikZ in the browser.

I played with web2js a couple of years ago. TeX ends up being a 500kb WASM file (88kb gzipped).

The LaTeX format file or the memory image after LaTeX is loaded are a bit bigger though (2.3 MB and 6.3MB gzipped, respectively).

Not OP, but do you mind me asking what advantages you hope to achieve by using WebAssembly rather than KaTeX?

Well, for one, KaTeX doesn't do "LaTeX" but a limited subset of the TeX equation syntax. As such, it can't handle more complicated macros or typesetting anything apart from equations.