Unable to sign in to your Apple ID. Try again later.

Here are a variety of resources helping with connectivity issues:

If you can't connect to the App Store, iTunes Store, or other Apple services, read this support article --> If you see "Cannot connect" - Apple Support

- If none of the suggestions work, try the last one: "If you’ve tried all of the above steps and you still can’t connect, contact Apple Support."

Here's a related article about what to do if you can't connect or sign in to iCloud --> If you can't connect or sign in to iCloud - Apple Support

If your iPhone or iPad won’t connect to a Wi-Fi network, or if you have related connectivity issues, read this support article --> If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

Here's a case where using a VPN prevented sign-in --> https://discussions.apple.com/thread/254836813?answerId=259008052022#259008052022

If none of the resources provide a solution, contact Apple for assistance:

For support, click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support

Try and completely stop iTunes, reboot your computer and try to log in again to see if the issue persists