The f is not an equivalency number. It's the actual f stop number. F number is the ratio of the lens focal length to the diameter of the entrance pupil and is independent of the size of said lens.
The depth of field on the other hand does depend on the size of the lens (or hence the size of the sensor the lens focuses it's incoming light on).
Let's take an 18mm F/2 lens on a Micro-Fourthirds camera. Those have a 2x ratio of sensor size compared to a full-frame sensor. So this 18mm lens would be an (2x18=36mm "equivalent") full-frame lens, meaning the perspective of said 18mm would be the same perspective a standard 35-36mm full frame lense would have. This 18mm F/2 lens would be F/2.0 based on the amount of light it lets in. That's the ratio of said lenses focal length to it's entrance pupil. Only in terms of "how the background will blur" we multiply this by 2 to show what the visual effect of this would be.
So really the best way of saying it would be "hey this is an 18mm/F2 Micro Four Thirds lens (36mm, F2/F4 equivalent).
Personal opinion: Even better if we used a different acronym for depth of field, say d or doF or something. Then we could say "36mm f2.0 DoF4.0"-equivalent lens.
So in the iPhone 14PM main camera case we'd call it a "28mm f1.78 DoF8.1"-equivalent as it has an about 4.6x sensor size crop factor from full frame.
The depth of field on the other hand does depend on the size of the lens (or hence the size of the sensor the lens focuses it's incoming light on).
Let's take an 18mm F/2 lens on a Micro-Fourthirds camera. Those have a 2x ratio of sensor size compared to a full-frame sensor. So this 18mm lens would be an (2x18=36mm "equivalent") full-frame lens, meaning the perspective of said 18mm would be the same perspective a standard 35-36mm full frame lense would have. This 18mm F/2 lens would be F/2.0 based on the amount of light it lets in. That's the ratio of said lenses focal length to it's entrance pupil. Only in terms of "how the background will blur" we multiply this by 2 to show what the visual effect of this would be.
So really the best way of saying it would be "hey this is an 18mm/F2 Micro Four Thirds lens (36mm, F2/F4 equivalent).
Personal opinion: Even better if we used a different acronym for depth of field, say d or doF or something. Then we could say "36mm f2.0 DoF4.0"-equivalent lens.
So in the iPhone 14PM main camera case we'd call it a "28mm f1.78 DoF8.1"-equivalent as it has an about 4.6x sensor size crop factor from full frame.