Which companies Open Source their website?

I'd be surprised if any appreciable number of websites could be considered "closed source". HTML and JS are quite hard to close off, being interpreted. WASM is a binary format, I guess, but that's still just a tiny tiny fraction of sites. Server-side stuff could be closed, but for most money-making sites the secret sauce is what's in the database rather than the code that shows it to you.

I would be surprised if they did, a website is essentially a representation of the company after all. Most wouldn't want anyone to be able to copy them that easily.

That said, you can usually look at the html code, but they would probably not license it to you.

Lichess: https://lichess.org/source