"No Service" on my iPhone after iOS 14.7.1 update

It will not be resolved with any upgrade, because it is not a problem with any version. It is a hardware or software problem with YOUR PHONE, not the version you have installed. I posted a troubleshooting article on the first page of this thread. Here it is again:

Go to Settings/General/About and look at Modem Firmware. Is the entry blank? If it is you need to reinstall it by restoring the phone to factory settings, then restoring a backup. Back up the phone first, of course:

1. How to back up your iPhone, iPad, and iPod touch - Apple Support
2. Restore your iPhone, iPad, or iPod to factory settings - Apple Support - follow the instructions to restore using your computer, do not using Settings/General/Reset (which is not included in those instructions)
3. Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If the modem firmware DOES have a value you probably have a hardware problem. The first step is what I just posted, but after that you need to contact Apple support using the Get Support link at the top of this page.