Schematic and Parts - 85 watt Magsafe 2 Power Adapter

Apple is not here, only end users like you. I doubt that any users here will have the information you need.

Jim, those pins are called spring loaded pins, often colloquially referred to as "pogo pins" for which there are a variety of suppliers. In addition to power another typical use is for JTAG connectors.

They are specified in a mind-boggling array of different inner and outer pin diameters, compressed and uncompressed lengths, maximum and minimum spring forces, tip shapes and dimensions, current limits, and materials.

The good news is they are not expensive, so order a variety and determine which best suits your needs. I can guarantee that determining the particular vendor Apple uses or their part numbers will be futile, but they almost certainly use more than one supplier.

For prototyping purposes I suggest using straight pins (no flange) inserted into a single inline header socket strip. You can push the pins into their respective sockets without concerns about soldering directly to the pins. Just be very careful about the socket dimensions. The pin diameter can be thousandth or two over that of the socket, and they will stay firmly in place. More than that and you won't be able to insert the pin. Too loose and they'll fall out.

Here is one supplier (not necessarily Apple's): https://www.emulation.com/catalog/pogo/

Your head will spin determining the parameters appropriate for your project. That's the hardest part. For frequent insertion and removal vs. one time testing (a typical application) I recommend using a hemispherical or concave tip shape. Sharp tips (serrated, trident, spear, hexagonal... ) make better contact especially with oxidized or contaminated surfaces but will eventually remove the plating, assuming the contact surfaces are plated.