Adam Engst, writing at TidBITS:

Apple seems allergic to saying that an iPhone won’t charge with MagSafe during Continuity Camera. However, it may not charge over USB either. Several users in a Reddit conversation reported that their iPhones lost charge during Continuity Camera sessions, even while plugged in.

I suspect that Continuity Camera taxes the processor sufficiently that the iPhone heats up. (It’s always warm when I take it off the mount after a meeting.) Since MagSafe charging also causes the iPhone to get warm — warmer than USB-based charging — Apple’s battery optimization system may be putting charging on hold to protect the battery from thermal overload. Which is good, if unexpected in the moment.