This is more or less correct. I'd be wary of talking about the 'equivalent aperture' on a full frame sensor though. A larger sensor does not, per se, mean that the ƒ number will be higher. The ƒ number is a property of the lens, not the sensor.
The thing is, using the ƒ number to compare the amount of light reaching the sensor only makes sense for lenses
with the same image circle radius. The ƒ number is directly related with the amount of light
per unit of area. That makes sense for comparing lenses used in full frame and APS-C cameras: all those lenses have the same image circle radius (the one that fits the 35mm sensor).
APS-C cameras just have a smaller sensor that doesn't cover the entire image circle. So that's why you don't get more light when moving from a full frame to an APS-C sensor on the same lens, and you don't have to make conversions to a 'equivalent' ƒ number.
What's happening on phone sensors? Well, since you're not dealing with a system with interchangeable lenses, the lenses themselves are designed to have an image circle that matches the size of the sensor, more or less. So the ƒ numbers still correctly represent the amount of light per unit of area, but the area may have changed.
Let's make an example:
- Phone A has a 1x1cm image sensor, and a lens with a 8mm focal length (real, not 35mm-equivalent), with an image circle with a radius R = 0.5cm, enough to just barely cover the entire sensor. The aperture has a diameter of 5mm. That means a ƒ/1.6 aperture (focal length / aperture diameter = 8mm / 5mm = 1.6).
- Phone B doubles every metric: you want a bigger, 2x2cm sensor. But the lens in Phone A doesn't cover the entire sensor (the image circle is too small), so you design a bigger lens, with 16mm focal length (and an image circle of R = 1cm) so it has the same field of view as before (same 35mm-equivalent focal length). Then, you also decide to give it an aperture of double the diameter: 10mm. That means the ƒ number stays the same: ƒ/1.6 (focal length / aperture diameter = 16mm / 10mm = 1.6).
But it'd be *very* wrong to say that the lens in Phone B let's in the same amount of light as the lens in Phone A. In fact, it lets in *four times* the amount of light in Phone A. The thing that remains constant between both phones is the amount of light per unit of area. But, if both phones had the same resolution, every single pixel in Phone B now receives *four times* more light than Phone A (because the pixels now have four times the area, and the amount of light per unit of area is constant).
What happened between the iPhone 13 Pro and the iPhone 14 Pro is more or less the same. Sensor grew in size (don't know how much), so the lens' focal length also had to, which meant that ƒ number would go up, unless the aperture diameter grew in the same ratio.
It looks like the aperture diameter didn't grow as much, but that doesn't mean the lens captures less light. It likely captures more light now, but it's now spread over a bigger area. That area simply has spread more than the amount of light captured has, so each unit of area receives less light, BUT the area is much bigger,
the total amount of light that the lens captures has likely gone up quite a bit.