What kind of document documents the following team practices/rules/procedures?

• Coding practices and syntax
• Directory structure and file naming conventions
• Testing plan (Unit, Integration and System)
• Logging rules and procedures
• Backup (of database, etc.) rules and procedures
• Adherence to module/component scope (functionality)

I am starting a new role that doesn't have any of these procedures. So I want to produce a document that says 'Every new software project needs to start with a Software Architecture & Design Document that explains and plans the ABOVE_THINGS' where ABOVE_THINGS = my bullet points above.

If I know the term for such a document I can google some templates to start me off.

You could call it Standards, although several of the things you list would be part of the
TDD (Technical Design Document). Backup plan would usually be part of the TDD. The test
plan is a separate document.

Search terms like "coding style", "project layout", "project rules", or "project guidelines" may be useful.

I would call that a coding style guide.

It's great to have such a document when working on a large project with a large team so that you don't get one person coding with tabs and cuddled braces and another coding with spaces to indent and braces on a newline, or someone using Hungarian notation for variables and someone else using javaCase...

Standards and Procedures?

You could call it Standards, although several of the things you list would be part of the
TDD (Technical Design Document). Backup plan would usually be part of the TDD. The test
plan is a separate document.

Yeah most of it is covered by TDD (or we call ours the TDO, but it's the same thing).
Our Technical Design Overview document starts with:
Purpose
Give a high level overview of all technologies required to make the game according to the game design. This document will list all systems, tools, 3^rd party technologies, and pipelines. This document will also provide a brief description of the engine and architecture, identify whether technologies used are new or existing, present the technology schedule and the engineering staff plans. The TDO will also point out risks of various areas of technology and possible mitigations for those risks including dependencies.
...and covers most of your bullet points.

In general, we call these kinds of procedure documents "bibles" -- e.g. the art bible, the coding bible.