Q: Photos doesn't update automatically

How are you transferring the photos from the iPhone to your Mac?  Are you using My Photo Stream or iCloud Photo Library?

• My Photo Stream will only transfer the photos after you close the camera.app, if the iPhone is connected to WI-Fi, and if it is properly charged.
• iCloud Photo Library can occasionally be slow.

This Support document states that the limit for battery power is 20%. So you should have been fine with 30%

Get help using My Photo Stream - Apple Support

1. See if your iOS device is below 20% battery power. If it is, My Photo Stream will be disabled temporarily to preserve battery life.

But the indicator can be inaccurate.

Give this a try:

Disable My Photo Stream  and iCloud Photo Sharing in the System/iCloud preference pane

and in Photo's iCloud preference pane.

Reboot and reenable both respectively. That should jump start Photo Stream.