There is, alas, no generally agreed set of documents (and their templates) that all companies follow. Some may employ a project management methodology like SSADM, Prince 2, Agile etc, but even then, it can be highly customized to the business.

What you're really describing here is what you've already alluded to - it is a technical document. What you put in here really depends on the type of project. Even if you design yourself a specific template, the sections will vary widely depending on whether you're writing a console app, a web application or whatever.

Maybe try getting a steer to see what else has been written already and try to follow that.

If you're really a trail blazer, you'll need to keep a firm hand on the document as various audiences will want all sorts of stuff added so you need to be careful it doesn't suddenly morph into a training document or user manual etc.