AirDrop does not use your home Wi-Fi network... It just needs to have the Bluetooth and Wi-Fi of both iPhones enabled/turned on...
Since iOS 16.1.1 [China] and iOS 16.2 [rest of the world] AirDrop is limited to 10 minutes for Everyone while no time restriction for Contacts only...
As you said, the video is more than 6GB so if the setting is Everyone on the receiving device, because of the 10 minute limit, the transfer may fail or just freeze...
Is the newer device using an Apple ID/iCloud account? If both devices are using the same account, you can set AirDrop on the receiving device to be Contacts only...
What version of macOS are you using? I'm not entirely sure but somewhere between Big Sur and the newer versions, the AirDrop time limit for Everyone was also introduced...
Since you have attempted AirDrop to another iPhone and to a Mac but both seem to fail, you can try downloading Send Anywhere from the App Store and use it in place of AirDrop... You just need to have both devices connected to the same Wi-Fi network...
You can either install Send Anywhere on both the iPhone 7 and iPhone 13 and perform the video transfer that way or use a 3rd device which is your Mac... Install Send Anywhere on your Mac, transfer from iPhone 7 to Mac then from Mac to iPhone 13... You need to have Send Anywhere installed on all devices that will be involved in the data transfer...
When I attempted transferring a large video file [about 50GB 4K60] using Send Anywhere, it failed so I had to resort to uploading it to OneDrive and download it to the other device using OneDrive app...
I have not tried this but you can use iTunes/Finder to transfer from iPhone 7 to your Mac then transfer from your Mac to iPhone 13... Almost the same as what I do except no 3rd party software involved...
