What you are asking could be the subject of a book.
Normally here we try to give answers but not write books. Content Controls can be linked or mapped to XML nodes but are not required to be so linked. The key through the user Interface is the Developer Tab and possibly the "document properties" found under Insert > Quick Parts which are discussed in the second reference link below.
That template could definitely be improved by using mapped content controls for information that is entered in multiple places. One of these could also be used to have the client name and other information in the footer or header.
Here are some references:
I recommend starting with the first three unless you are already into VSTO solutions. They show how to work through the user interface of Word rather than external coding.
Here are free Add-Ins that make mapping Content Controls relatively simple. They are from Greg Maxey and Graham Mayor.
Other Thoughts
In your question, you are conflating variables, fields, and Content Controls. My answer deals with Content Controls, which are not fields and which can relate to variable information. Here is a list of the usual Word Fields with links to documentation. Document Properties can also hold variable information which can be shown in a DocProperty Field. These document properties are different, though from the ones discussed in my article and are not linked or mapped to XML.
Work on Content Controls through the User Interface is best done using the Windows desktop application
The Macintosh interface currently does not encompass creation or modification of Content Controls. It can be done through vba, though. At some point this may change but it has been more than ten years waiting for Microsoft to add this to their Mac versions. (March 2022) Content Controls for the Mac OS by John Korchok