apple tv is not accepting air play from my new iphone 14

What are you trying to stream? Unfortunately, not all content is compatible with AirPlay. Content providers can choose to not support AirPlay.

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

3)software updated

Apple TV 4K, tvOS 13

Apple TV 4K can be updated to tvOS 16.1, so the unit as mentioned in your post sig, seems not updated. Please verify. Update your Apple TV - Apple Support. I don’t think it wouldn’t matter for AirPlay, though.

the provider has an icon for air play

Like this?

Other streaming protocols may have different icons.

… and seems to connect to other devices but not to apple TV.

AirPlay should see for destination devices: Apple TV boxes, AirPlay-2 enabled TVs, AirPlay 2-enabled Rokus, modern Macs – if access is available to you (often: on your own home network). If you see different devices, then it may not be about AirPlay.

my network speed is between 2-8 MB.

My FIFA stream seems to be about 2.5 Mbps for 1080p HD, which is low compared to streaming movies. 8 Mbps should be adequate in all cases.