Airplay issue on second generation apple tv

The 2010 model Apple TV (2nd generation) will not be sufficient for AirPlay for some services. Some services (or apps) require a later model Apple TV: 3rd generation or later, or maybe: 4th generation or later. Some services will not support AirPlay at all to any device.

E.g. Disney+ requires Apple TV (3rd generation or later) for AirPlay.

E.g. Apple TV+ requires Apple TV (3rd generation or later) for AirPlay.

E.g. Netflix does not support AirPlay at all.

If you can AirPlay screen mirror the home screen of your iPhone or iPad, or desktop from your Mac, then AirPlay itself is working as good as it can.

Use AirPlay to stream video or mirror the screen of your iPhone, iPad, or iPod touch - Apple Support

If screen mirroring or streaming isn't working on your AirPlay-compatible device - Apple Support

AirPlay system requirements - Apple Support

You have not specified from what device(s) you are trying to AirPlay. And what version system software these AirPlay source devices use.

For AirPlay, all devices communicating with each other, have to be connected to the same home network. Are they?

If you use a different SSID network name for the 2.4 GHz band and for the 5 GHz band, then those would be seen as separate networks, and devices on one would not be able to connect with devices on the other. Instead, have your router combine them under one name. Recommended settings for Wi-Fi routers and access points - Apple Support