Emscripten: Make the web example work again

[hoodmane]

My recent changes to the Emscripten build broke the web example. I'll fix it and also move all of the components of the web example into a subfolder under Tools/wasm/emscripten.

Linked PRs

• gh-127111: Emscripten Make web example work again #127113
• gh-127111: Apply prettier formatter to Emscripten web example #127551
• gh-127111: Emscripten Move link flags from LDFLAGS_NODIST to LINKFORSHARED #127666

[freakboy3742]

This also requires the changes to the CLI script from #127506 before it can be closed.