iPhone 13 stuck on reboot loop after 15.4.1 update

Greetings, ky1ia11.

When you say that your iPhone is stuck in a reboot loop, do you mean that you see the restore screen? This screen shows a computer and cable. 

If so, check out these steps:

“If you see the Restore screen:

1. Connect your device to your computer using the cable that came with your device. Don't disconnect your device from your computer.
2. Restart your device:

• iPhone 8 or later: Press and quickly release the volume up button. Press and quickly release the volume down button. Press and hold the side button until you see the Apple logo.' If you see the Restore screen on your iPhone, iPad, or iPod touch 

“Reinstall iOS or iPadOS

If you still see the Restore screen after you restart, you need to reinstall iOS or iPadOS:

1. On your Mac, make sure that you've installed the latest software updates (including iTunes if you have MacOS Mojave or earlier). Or on your Windows PC, make sure that you've installed the latest version of iTunes.
2. Make sure that your device is still connected to your computer. You should see this message: "There's a problem with the [your device name] that requires it to be updated or restored."
3. Click Update (not Restore) to reinstall iOS or iPadOS and keep your personal data. Don't disconnect your device from your computer until the update finishes.” If you see the Restore screen on your iPhone, iPad, or iPod touch 

Should our understanding of the issue be incorrect, consider offering additional information to help us understand what you are experiencing. Be sure to include any error messages, as they can be helpful in diagnosing the issue.

We hope this helps! 

Sincerely.