I am looking for a good host that supports all the dependencies of PressBooks. So far, they have been telling me that shared hosting is not an option if I want to install the 3rd party libraries (dependencies). Would appreciate hearing any suggestions.
My advice is just make sure you do your homework and make sure they agree to do ALL dependencies.
I have a self hosted server on AWS where I had to do all the work, and a managed hosted server using Reclaim Hosting. They support almost all the dependencies, except they refused to support mathjax. For accessibility purposes, and the ability to create math PDFs that was disappointing. In SUNY, our largest pressbooks server is managed by Lumen Learning, but they prioritize the HTML version of the book over all else so they refuse to use PrinceXML exports, because they prefer ePub and HTML documents.
The honest truth is you should probably reach out to Pressbooks themselves and see what you can work out. No one will support pressbooks better than the pressbooks team.
You should get very good linux administrator and get any virtual server from good provider, I would recommend DigitalOcean, You can install all dependencies required.
Having a good linux administrator handy will be a great advantage.