Broken iPhone 13 with back damage and connectivity issues

You'll need to schedule an appointment at your Apple Store Genius Bar and Apple will tell you if the phone can be saved or not. My guess is your phone sustained too much damage to be saved, but Apple will need to see the phone.

Genius Bar Reservation and Apple Support Options - Apple

Simple crazed back screen may be savable but if it separated it isn’t rally economically viable IMO.

Get a quote https://support.apple.com

In all likelihood, the device will have to be completely replaced. In the case of an iPhone 13, that's $449 if you don't have AppleCare+. For $499 you can buy a new iPhone 16e. For $599 you can buy a new iPhone 16.

I would not consider it financially smart to replace your 13 with another 13 if you don't have AppleCare+.

"Broken iPhone 13 with back damage and connectivity issues: I dropped my iPhone thirteen without a case from a very tall place, and it landed on the back and basically smashed. The back of the iPhone is lifting, and I am unable to connect to the internet or use wifi, as well as use cellular. Is it scrap or is there potential to save it?"

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Using an OtterBox and Liquid Fixes:

Take the as a learning experience, knowing to use a cover; OtterBox being a superb example. And, as long as it's not covered by AppleCare, then look into using liquid fixes. I've had my iPhone 13 Pro Max for literally years, and not a ding is on it when taken out of the case.

Note:

Placing liquid fixes to the iPhone's screen (i.e. Liquid Nano or Liquid Armor) would cancel your AppleCare coverage. So, avoid using it, if you have AppleCare on your iPhone.