The headless Obsidian Sync client works the same way as desktop and mobile clients, see:

https://help.obsidian.md/sync/troubleshoot

- Markdown files: Obsidian Sync merges the changes using Google's diff-match-patch algorithm.

- Other file types: For all other files, including canvases, Obsidian uses a "last modified wins" approach. The most recently modified version replaces earlier versions.

For conflicts in Obsidian settings, such as plugin settings, Obsidian Sync merges the JSON files. It applies keys from the local JSON on top of the remote JSON.