AirPlay to Samsung smart tv?

Those steps work for any device. If the Samsung Tv does not show up in the Airplay Menu or Screen Mirroring, then the Tv may not be Airplay compatible.

As I said check that the particular model of Samsung TV is Airplay compatible.

This Airplay feature to non Apple devices is fairly new. It would not have been available years ago, and would likely not be supported on Samsung TVs that are more than 3 or 4 years old at this point.

From the link I provided above, here are the supported Samsung models:

Samsung

• Samsung FHD/HD 4, 5 Series (2018)
• Samsung QLED 4K Q6, Q7, Q8, Q9 Series (2018, 2019, 2020)
• Samsung QLED 8K Q9 Series (2019, 2020)
• Samsung The Frame Series (2018, 2019, 2020)
• Samsung Serif Series (2019, 2020)
• Samsung UHD 6, 7, 8 Series (2018, 2019, 2020)

2021 and 2022 models should also be supported.

I can tell you those steps work for me with my Samsung TV. There are no special steps for Samsung. The steps are the same for all devices that support AirPlay.

If you can explain where your nephew is getting hung up, maybe we can provide more specific advice.

Follow the steps in the support document you posted from, and select your TV from the list in the Screen Mirroring or Ariplay menu as explained in the support document you posted from.

If you are having a specific issue, then explain what that is.

Make sure your Samsung TV is one of the supported models for AirPlay. See the "AirPlay 2 enabled Tvs and devices" section here: Link-> Apple TV app and Airplay enabled - Devices - Apple