Apple - How can I use my iPhone 7 to take photos remotely?

You can indeed use Bluetooth headphones for taking photos with the built-in iOS Camera app. In fact, it doesn’t even have to be headphones, so long as the device has volume controls.

However, here’s the catch:- The volume controls of the Bluetooth device have to control the iPhone’s built-in volume (i.e. they control the volume levels of their own speakers via the iPhone's built-in volume control rather than directly changing the volume of the speakers within the earphones/headphones). Unfortunately, many of them do not do this, and that's why any Bluetooth keyboard with volume controls will work as they don't have their own speakers, so can only control the volume at the iPhone end.

My recommendation is to use a dedicated remote for this purpose, such as the HISY Bluetooth Camera Remote. This device is designed specifically for this purpose and can be used for both taking photos and videos, and from a distance of up to about 27 metres (90 feet).

Note: I have no affiliation whatsoever with this product.

Since the title of the question is about taking photos remotely, rather than specifically about Bluetooth headphones, I’ll point out that this is also possible using an WATCH.

The Camera app that ships with watchOS lets you do a lot more than activate the shutter button remotely. It provides a viewfinder for the iPhone’s camera, so you can check how your final photo will look before taking the shot, and it also lets you switch between different modes, toggle Live Photo and HDR, and set a timer.