This project has not been tested with every contributed module, but this page will categorize ones that are known to have problems

• Views - Publicly accessible exposed forms, contextual filters (using query params), and AJAX does not work with Tome, since there is no Drupal site running to support them. Pagers on non-AJAX forms are supported, with some magic.
• Search - Search API and most search modules rely on a Drupal backend to find a deliver results, and as such they are not compatible with Tome. For basic, free search functionality it's recommended that you use Lunr search, a Drupal module that creates a JSON index of your content based on a View, and does search client-side.
• Most forms - You should not expect any publicly accessible form to work on your static site. It's static HTML, there's nowhere to POST! 😄It's recommended that these dynamic elements are moved to a PaaS service or DIY serverless function. If you use Netlify, the Tome Netlify module will let you submit core Contact Forms to Netlify with minimal setup.
• Paragraphs - When a Paragraph is removed from a field, it is never actually deleted. This can lead to a lot of stale entities in  your repository, which you would normally have to manually clean up. The "Paragraphs Clean" contributed module will delete Paragraphs when they are unreferenced. I use it on this site and it seems to work OK.