I am also experiencing this issue. If the Obsidian app is already running, then using obsidian://open?vault=MyVault to switch to a different vault will appear to do nothing, and I’ll remain in my current vault, viewing my current note.
As soon as I tap the vault switcher icon, it will very briefly flash the vault switcher screen and then automatically switch to the vault previously specified in the URL, and show me the last note I had been viewing from the specified vault.
From now on, every time I tap the vault switcher icon, it does the same thing, giving me no opportunity to select a different vault via the switcher screen.
However, if I run a different shortcut URL such as obsidian://open?vault=MyVault2, the same thing will happen. I will seem to remain in vault 1, but as soon as I tap the vault switcher icon, it will very briefly flash the vault switcher screen and then take me to my last viewed note in MyVault2. It will then remain stuck on MyVault2 until I either kill the app or run yet another shortcut URL to force it to switch to another vault (and remain stuck there).
I’m on the very latest public release of Obsidian mobile 1.1.0 (38) on iOS 15.3.1