I had a similar issue and after much back and forth found out this is an issue that affects a small number of iPhone 7s. Apple support has a page about this: https://support.apple.com/iphone-7-no-service
I'm copying the text below:
Apple has determined that a small percentage of iPhone 7 devices may show "No Service" in the status bar (even if cellular coverage is available), due to a component that has failed on the main logic board.
These affected units were manufactured between September 2016 and February 2018 and sold in China mainland, Hong Kong, Japan, Macao, and the U.S. See below for iPhone 7 model numbers that are covered in this program.
If your device exhibits the symptom described above, Apple will repair your device, free of charge. Your iPhone will be examined prior to any service to verify that it is eligible for this program. This program only applies to iPhone 7.
Apple will be contacting customers via email who may have paid for a repair related to this issue to arrange for reimbursement. If you believe you paid for a repair related to this issue, and have not received an email from Apple by the end of March 2018, please contact Apple.
Below are the three model numbers that are eligible for this program. You can find the model number on the back of your iPhone 7.
Eligible Models
Model number Country/Region
A1660, A1780 China
A1660 Hong Kong Macao U.S. (includes Puerto Rico and U.S. Virgin Islands)
A1779 Japan