Personally, after churning through all the static site generator options, I landed on Jekyll, one of the first of them. It’s definitely not the sexiest solution, but it’s Markdown-in and HTML-out (my main page is still raw HTML/CSS from like twenty years ago, though), was the easiest for me to match the styling that I wanted from the base theme, and it’s been along for long enough that it’s mostly surprise-free.
That said, if you only want the equivalent of a business card, I might argue that setting up anything is probably overkill, all overhead for just a tiny bit of content. In that case, you can grab some modern-ish HTML boilerplate like this one, then use Pandoc to convert the Markdown (which you presumably already know if you’re messing with Hugo) to the HTML that goes between <body> and </body> in the boilerplate. Add CSS, and you’re done.
Oh, and actually, depending on how broadly you want just the “business card” idea, something like Littlelink might also fit your needs, where you hack out the links that you don’t care about and fill in destinations for the rest.
That’s close to how I think about it, yeah, but I’d push more in terms of the investment. Since Jekyll, Hugo, Svelte, Eleventy, and the rest just generate flat HTML to upload, there’s nothing wrong with using it for a single page. But you end up needing to learn the whole build-and-deploy process and all the layout quirks, which (especially if you’re starting from scratch) will take longer to get the page out. And like you point out, the more material you have, the better that investment looks.
But then, if you already know the system, there’s no new investment, so it becomes more of a toss-up whether to build things that way, since a page of Markdown is slightly faster to write than the equivalent HTML.