Would there be any negative effects from uploading German content (job advertisement) to a page template that's tagged up as being in English?
We will not be able to edit the meta tags to signal that this page isn't in English.
There should not be any negative effects if the majority of the content is in English.
According to Google:
Google uses only the visible content of your page to determine its language. We don’t use any code-level language information such as lang attributes. You can help Google determine the language correctly by using a single language for content and navigation on each page, and by avoiding side-by-side translations.
As a result, I would make sure that all content other than the advertisement is in English.