For false sync conflicts see this bug report: Obsidian Sync: Conflict File generated but user has not independently modified on multiple devices.
As a workaround to avoid bad merges while the duplication bug exists, you might consider setting Sync to use conflict files instead of automatic merging.
If foreground sync is completely unworkable for you, you may want to consider another sync solution (iCloud would be a natural choice). Sync syncs very often, tho. If it hasn’t started syncing when you want to close the app, it’s probably about to. I understand that those little waits add friction and frustration. A workaround is to put the phone away without closing it. It will lock automatically after a short time, and unless there is a large amount to sync, Sync is likely to finish before then.
In the meantime there is a feature request for background sync which you can support: Make Obsidian Sync work in background (on Mobile).
The discussion there explains the difficulty in implementing it.