Unable to view videos on iPhone ‘try again later’ error

Do you have a 3rd party VPN installed, even if you are not using it? If so, delete the VPN profile in Settings/General/VPN & Device Management/VPN. Don't just turn it off; delete the profile. If that fixes it, you can try reinstalling VPN. However, VPN actually reduces your privacy, it does not enhance it.

I can recommend, firstly, as Lawrence Finch said, disable VPN if you are using one.

You may additioanlly check for the restrictions: Settings > Screen Time > Content & Privacy Restrictions and ensure YouTube is not restricted.

Try to access YouTube through the Safari broswer to determine if the issue is specific to the app or not.

As a last resort, reset network settings: Settings > General > Transfer or Reset iPhone > Reset > Reset Network Settings. (Note that this will erase saved Wi-Fi passwords.)