Raindrop web, mobile, and desktop apps are on Github [1], none of the repos have licenses though. It has support for Dropbox and Google Drive backups [2].

1. https://github.com/raindropio

2. https://help.raindrop.io/backups#automatic

BrainTool[1] is a similar bookmarking extension that is open source[2] and syncs data to a plain text file (org-mode format) on Google Drive.

[1] https://braintool.org [2] https://github.com/tconfrey/BrainTool