The tool actually is open source, so you could self-host it if you wish. MIT license, in Python. The repository [1] is linked in the blog post the author wrote about the project [2].
The open source version is a bit different from the hosted one: the open source code involves running the polling script, then building a static site (which is how I run the site for several months as a single-user project).
I am planning to move the polling changes upstream soon and then figure out a plan for open sourcing the full project.
[1]: https://github.com/capjamesg/web-reader
[2]: https://jamesg.blog/2024/11/30/designing-a-calm-web-reader/