I’m using syncthing, but I think I recall the sort of issue you mention. Android locks down cross-app access quite hard, but if you move the files to your SD card (or tge emulated one if you don’t have one) it acts as shared storage and your sync program and obsidian can both read and write to it. On my device, the path is /storage/emulated/0/Documents/<whatever>

You can sync Obsidian yourself too, it’s just a bunch of files, so anything that’ll handle them works.