Parser gets confused when a new section begins on a new page

I am using latex with a custom style to build PDFs -> https://www.overleaf.com/latex/templates/mtecks-resume/fzgztpkgngjc

This was working reasonably well, until an edge case. Whenever a new section starts on a new page, that section gets merged with the content that ended on the previous page.

I've been trying to figure this out for months and even offered a bounty, and thought the root problem was something related to how TeX handles blocks of text, as opposed to streams. The more I look, the more it seems like the problem is the parser losing some sort of context on a page reset.

Hopefully this screenshot makes the issue obvious.

This happens no matter how the previous page ended. It could be a single word, or paragraph, fully left-aligned, and the problem always happens. I can trick this into working by placing a white period '.' on the line above a new section and then hide it using vspace{-1em} and the parser will then do the correct thing, only when that '.' is the first thing on the new page. Any other time, it gets merged with the heading.