First, "Quick Parts" is a confusing term because MS really messed up when naming it.
Quick Parts on the Insert Tab has several distinct parts that bear little relationship to one another: - Quick Parts building Blocks - If you add something to Quick Parts Gallery it is a "building block." It shows up on the Quick Parts Gallery in that menu. It is only one of 35 building blocks galleries. Building Blocks & AutoText by Greg Maxey You can use all of the galleries.
- AutoText - This is another building blocks gallery and the original one. It is the only one that can be used in the Mac versions of Word.
- Document Property (Content Controls) - again a mishmash of a term. See my page Repeating Data Using Document Property Content Controls and Other Mapped Content Controls and Enhanced Document Properties AddIn by Greg Maxey.
- Fields - These date back to Word 97, at least, and have not changed much. Paul Edstein has a number of pinned tutorials here on fields.
- The Building Blocks Organizer - intended to give more control over all building blocks to the user. Greg Maxey has a Building Blocks Add-In at the bottom of his page that is an enhanced version of this.
With that stated, Building Blocks are stored in Templates.
Where can Building Blocks be stored?
Building blocks can be as little as a word or a symbol and can be multiple pages and
sections. As far as I know, they can contain anything that a Word document can contain. Look at
Build & Deploy Custom Building Block Galleries by Greg Maxey. Those can be in individual document templates or in
Global Templates available in all documents. A simple example of using a custom gallery and including a drop-down for it in the QAT can be found in my
2003 WordArt Add-In for 2010-2019 (365).
A very powerful tool to use with building blocks is the Building Blocks Gallery Content Control. Another is the AutoTextList field.
(Even though it says "AutoText" it works with any building block.) AutoText Menus in your document - Incorporating AutoText or other Building Blocks in Templates
I think building blocks can do everything you want. I would not be using the Quick Parts building blocks gallery for them, though. I would certainly examine this feature more closely before trying to create something else.