Powering iPhone 16 Pro Max with USB-C Digital AV Adapter

Sure. The USB-C Digital AV Multipoint Adapter has a USB-C port that is specifically intended to be used to provide power from a USB-C power source - such as your USB-C Power Adapter that you use to charge your iPhone.

When connected to external power via the Adapter, the iPhone will charge just as it would when directly connected to the Power Adapter.

Not sure where you're going with the "power supply work in reverse order". A USB-C connector is simply a connection type; the connector itself is bidirectional and does not of itself determine the direction that power flows.

USB-C Power Adapters supply power to the device to which it is connected. USB-C devices, such as your iPhone, will supply limited power from their internal battery to connected accessories, such as the USB-C Digital AV Adapter. However, this Adapter allows power to flow in the opposite direction, to charge the iPhone, when connected to a suitable USB-C power source.

In most countries/regions, Apple no longer includes a Power Adapter in the box with its devices. In those regions where the Power Adapter is now an additional cost accessory, the device cost is reportedly reduced to reflect this deletion from the box.

As outlined by MrHoffman, most models of iPhone will optimally charge when used with a 30W USB-C Power Adapter that supports USB PD (Power Delivery). These are sufficiently powerful to optimally fast-charge your iPhone - and can provide adequate power for both the iPhone and a connected Adapter that supports pass-through power. Lower power options can also be used, but will reduce the effective charging rate.

Andrey_Kazak wrote:

Does the power supply work in reverse order, that is if the power is supplied to female connector and consumed from the male connector?

USB-C Digital AV Multiport Adapter - Apple

"Use the standard USB port to connect devices such as your flash drive or camera or a USB cable for syncing and charging your iOS devices. You can also connect a charging cable to the USB-C port to charge your Mac, iPad, or iPhone."

Compared to the USB-C ports on modern Macs – which support USB, USB4, DisplayPort, and Thunderbolt – the USB-C port on this adapter is a "one-trick pony". It's there so that you can charge your iPhone at the same time that you are sending HDMI video to a TV or monitor, or using an external drive or card reader.

With USB-C Power Delivery, negotiations will go on behind the scenes as to the direction in which to supply the power, and the voltages to be used. The USB-C Power Brick will want to supply power, not consume it, and in this context, the iPhone will decide to consume power, rather than supplying it.

Charge and connect with the USB-C connector on your iPhone - Apple Support

Apple stopped including power supplies with iPhone a while back, as many were just getting immediately trashed, given many (most?) folks already had one or more they preferred and could reuse.

Apple recommends 18W or higher for wired fast charging, and recommends 30W for wireless fast charging:

• Fast charge your iPhone - Apple Support

Most any USB-C charger with Power Delivery (PD) will work.

I’ve had success with a variety of power supply options and cables including Apple, Anker, Klein, and others.