I suggest that you ask Claude Code to build such a website for you with a minimal set of features, with tons and tons of comments and design/architecture documents plus tests. Once that is done, you can start reading the code. You can even read as it is working.
Then, you can point Claude Code to a file/a function/a few lines and ask follow-up questions.
After that, there are even more things to do.
If you want a different perspective, you could try completely reimplementing the thing. My guess is that Claude will use Next.js. You can ask Claude not to do that but instead use a different UI framework/no framework combined with C#, if that's something you are interested in. If you want to actually learn all the details, you can start setting things up yourself and write the website. You can add features or try making the site scalable, under AI-assisted or vibe coding mode.
It will not produce the most elegant code or have the best architecture, but will be good enough for your purpose. I think it's the most efficient way to get some learning that is specifically suited to your needs in this age.