Since Obsidian and Jekyll both use Markdown, you can create a Jekyll project, open it as an Obsidian vault. You could then use Jekyll to run it as a web server on your own machine. (It also works nicely with Github Pages for public websites, since that has built-in Jekyll support.)

There's also a third-party Jekyll theme specifically for this purpose (https://github.com/Jekyll-Garden/jekyll-garden.github.io).