Building blocks are stored in templates, not documents. By default they are stored in the normal template, but you can choose instead to save the building block in any open template or installed add-in template. There is also a BuildingBlocks template which stores the default building blocks provided with Word.

Building blocks can be called from any template that contains them that is loaded into Word, either as an add-in or because you have created a document from that template.

The building blocks organizer will allow you to move a building block from its current location to any other open or loaded template by selecting the block and using the edit function to save it in a different location. Similarly when you save a building block by selecting the content and pressing ALT+F3 you can choose where to save it without having to first save it in the normal template.

Where you store the building blocks depends on where they are to be used and by whom. For specific documents, save them in the document templates. For use just by you on all documents, save them in the normal template or the buildingblocks template. For use by others, save them in an add-in template and make that template available to the others.

Greg has a couple of Building Block utilities on his web site which may prove helpful - such as https://gregmaxey.com/word_tip_pages...galleries.html