How old is my iPhone 7?

According to MacTracker, Apple introduced the iPhone 7 in September 2016. That would have been about eight and a half years ago. At that time, it was running iOS 10. Apple discontinued the iPhone 7 in September 2019.

I do not know if that is the worldwide discontinuation date, or just the one for the U.S.

I suspect that if you ever need hardware service, or battery replacement service, the availability of that will depend on the model, rather than on the date when Apple manufactured your particular iPhone 7.

Obtaining service for your Apple product after an expired warranty - Apple Support

As far as battery replacement service goes, Apple still offers that for the iPhone 7. They even offer it for the iPhone 6s and 6s Plus, which came out a year before your phone did.

iPhone Battery Replacement - Apple Support

That iPhone 7 uses an older serial number format, meaning you can decode the week of manufacture, and other data.

Details: https://en.tab-tv.com/serial-number-iphone-decode-explained-2010-2019/

Or more generally, there are newer iPhones that fell off current iOS support after that iPhone 7 fell off iOS support.

It’s also older than the three most recent iOS versions, which means various apps won’t work that far back.

iPhone 7 was introduced in Sept 2016 and discontinued in Sept 2019.

So, about 6-8 years old depending on when it was purchased.