SFDX officially supports tracking of source within the same package in more than one folder. The "standard" folder may be used, but you are also able to create a folder hierarchy that's more akin to a "modularization"

It can for example look like this:

force-app (any names goes here)
-> main
--> default
----> aura / classes / pages
-> module1
--> aura/classes/pages
-> module2
--> aura/classes/pages

Currently, only the metadata inside the force-app/main/default folder is seen. It would amazing if git integration could take other folders into account too. Both for Deployments from and to Git (for a deployment to Git, you would need to select the destination folder beforehand)