Since v16/v1.4 the tabs and last opened files are written in two different preference files:
workspace.json (for desktop app) and
workspace-mobile.json (for mobile app). Because of this the tabs and last opened files are not synced between desktop and mobile apps when using third party sync provider (iCloud, for example).
Please, move tabs and latest files into separate preference files like starred notes (for example).
Obsidian v16, Obsidian Mobile v1.4