Sounds to me like they're not trying to create a website for now, but rather just process some data, which they can later display in a static webpage.

So, I'm guessing something like this:

+--------+     +---------+     +----------+
| Static |     | Their   |     | External |
| Web    |---->| Own     |---->| API      |
| Page   |     | Backend |     |          |
+--------+     +---------+     +----------+

But yes, unless there's a lot of data to crunch, the design one would usually go for is rather:

+-----------+     +----------+
| *Dynamic* |     | External |
| Web       |---->| API      |
| Page      |     |          |
+-----------+     +----------+

So, the data calculations would happen in the user's browser. You would still need some hosting for that webpage, but there's lots of free services to put a simple webpage up.

And yes, when you go with that latter design, then JavaScript would be the typical choice. It's still possible to do it with Rust, using WebAssembly (e.g. a colleague of mine has built a small statistics webpage which gets data directly from GitHub, using the Leptos framework), but it is definitely the less beaten path.

Having said all that, frankly, fuck the usual way of doing things. If you're comfortable with Hugo for frontend work, then I think it's legit to build a little backend to take over the dynamic part. Better to build a useful project and learn something than to get stuck trying to learn the 'correct' path of doing it. Especially if you'd rather learn about Rust than JS.