I can copy text on my iPhone and see the bar on my Mac indicating that it’s being transferred, but then it won’t paste into Obsidian on my Mac. But it will paste into other apps, so I end up having to paste it into another (Mac) text editor, copy it again from there, and then paste that into Obsidian.
Oddly enough, it does work the other way around—I can copy text on my Mac and it will paste directly into Obsidian on my iPhone.
I’m using macOS Ventura 13.2 and iOS 16.3, both with the current stable versions of Obsidian and an up-to-date installer on macOS.
A related but Safari-specific bug was reported last year.