Possible few solutions are:
- https://github.com/mathieudutour/gatsby-digital-garden (Built on Gatsby)
- https://github.com/raghuveerdotnet/simply-jekyll (Built on Hugo)
- https://github.com/aengusmcmillin/gatsby-theme-brain (Built on Gatsby)
In all three, you commit your changes to Github and then let Netlify take a build and publish your content.
All of these generate backlinks when you publish. However, none of the above solutions were built keeping Obsidian in mind.
Gatsby Digital Garden was built to import and publish content from Roam. It also has a graph view. It displays transcluded text in backlinks when content is imported from Roam but not when content is authored elsewhere in markdown.
Simply Jekyll uses [[ ]] for wiki like links, and therefore can be used for publishing content authored in Obsidian. However, it also uses [[ ]] for many of its other nifty functionalities. So, you have to either let go of those functionalities or stop using Obsidian as the text editor. VS Code with Notecomplete plugin works. It is also the only one that has search built in. Check out https://www.raghuveer.net, personal blog site of the author of Simply Jekyll.
Gatsby Theme Brain does not provide either a graph view or even a list of topic. Also, it picks up topic title from the YAML frontmatter.
None of these currently support [[Actual Topic Title|Desired Display Text]] or [[Topic Title#Heading]] links. And I am not sure if any of these can be used to selectively publish topics.