@WhiteNoise Okay, thank you so much for identifying that. I have now reinstalled the mobile apps and named the vault on my mobile devices the same as the vault is named on my desktop, and it solved the problem. Thank you for the support.
Background:
I remember looking at these two pieces of advice, when setting it up initially, so maybe it would help others to specify on those pages, that the mobile vaults should have the same vault names as on the desktop:
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Obsidian Mobile - it says “create a new empty local vault”, so I did not figure out it should have the same name as the desktop vault.
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The advice in this post Obsidian Mobile Sync instructions, which was very helpful for me to get started. In step 8 it says “create a name for your vault on your iOS device (e.g. My Obsidian iPad)”, which I interpreted as the vault on each of my mobile devices should have their own names.