Problem
Automatic Table of Contents Obsidian plugin doesn’t get rendered correctly when being exported with obsidian-export. This is something I will need to work on probably adding functionality for this in an obsidian-export fork. This will probably also tie into Dataview Plugin Bug. I have discussed this plan with Nick Groenen the creator of obsidian-export. He has a similar workflow using a similar plugin obsidian-plugin-dynamic-toc. He shared with me his custom postProcessor for this as an example to build off of for my use case.
Solution
My plan for right now is to not fix this bug. Quartz already has a table of contents on the right side of every file so having one at the top is not needed. If I ever switch away from Quartz I will need to re-visit this problem.