Sorry, this isn't really going to provide a solution to a problem I experience a great deal. There really is no solution to this which I'm aware of.
This is really the same for any "styles" feature in any Adobe application - Graphic Styles, Paragraph Styles, Character Styles, object Styles, Table Styles, Layer Styles, etc. in Photoshop, InDesign, Illustrator, etc...
Each document is wholly independent in terms of style definitions.
Think about things in reverse..
What if all documents which used a particular style did update when you change a style anywhere? You would possibly find that file you worked on last year gets the style updated and completely ruins the overall design merely because you happened to name two very different styles the same name. Forcing you to fix the file due to the updates. Isn't it better to close a file and know it's going to stay the way you left it?
When updating a style, that updated definition will need to be re-imported into any file already using that definition if you want the style updated. And then artwork may need to be relinked to the internal style. It's just how things work. But you already know this.
For Illustrator Graphic Styles, they are customarily saved as an .ai file. So, when I change a graphic style, at that same time I open the style file and update there.. then go back through existing files to update artwork. It's a pain, I know. And I'm not arguing that this is by any means the best method. It's just the only method I'm aware of.
One possibly helpful tip is to create a "master project styles" file. I create a separate .ai file that contains all Graphic, Paragraph, and Character styles, brushes, swatches, etc for a project. I can then open that "master" file in the various panels to load those "master" items into the individual project files. Load it via the Brushes Panel and the brushes load.. load it via the Graphic Styles Panel and the styles load, etc. Not ideal, but at least it keeps all the definitions for everything in one place.
I have mentioned this to Adobe a few times. When working on something with 20-30 different files, heck even 5 files, all needing the same Graphic Style (or really any type of style) it's such a nightmare to have to track everything again when you change a style.
It would be nice if you could link to a style definition file and have them auto-update the same way you can link to images which then auto-update -- some sort of global definitions option. Unfortunately, at this time, that just doesn't exist. The best you can do is use the CC Library panel to store definition files (but only Paragraph and Character definitions) or an object which is styles how you want a Graphic Style to appear -- then update local Graphic Styles based upon that stored object after dragging to the artboard. To me, that's a far cry from a workable solution because it merely changes where the file is stored, not how the file is linked to.