How do I update my iPhone 7 Plus to iOS 16?

You might want to do this, but you cannot do this.

If you want to run iOS 16, you need an iPhone 8, iPhone 8 Plus or iPhone X.

But, since you will be looking for a new phone, it would make more sense to look for a newer model that can run iOS 18, like an iPhone 15 or 16

If you want to run something higher than iOS 15, it is time to purchase a new or newer iPhone. Preferably a phone that is compatible with iOS 18 now, and will be compatible with iOS 26 when that comes out this fall.

Note that only the 15 Pro, 15 Pro Max, and 16-series phones are compatible with Apple Intelligence.

No

In case you are thinking of purchasing a used iPhone, see

The All Too Common SAD Reality of Buying a Used iPad/iPhone – Apple Community

If you want to buy a preowned iPhone - Apple Support