No!
I am afraid that this is a common fallacy. The size of a lens is determined by its focal length and maximum aperture, not the size of the sensor it is designed for.
Actually sensor size matters because image circle size matters and optical design to the sensor format matters.
On a lens that goes to 200mm the front of the lens has to be 200mm from the sensor to focus at infinity - that is how focal length is defined.
Yes, when it is a pinhole camera....
Since the back of the lens is 44mm from the sensor the lens has to be around 160mm in length. An extended lens can be shorter when folded down, but at 200mm it still has to be about 160mm long.
False.
A focal length is calculated from the focal points, not from the physical lengths.
This is a reason why a mirrorlenses exists and can be used as physical size can be get shortened radically.
Same way is with other lenses that length can be shorter than their actual focal length without any mirrors.
The diameter of the entrance pupil is determined by the focal length and the f/ number by the ratio f/ = focal length/entrance diameter. So the diameter of the entrance pupil on a 70-200mm f/2.8 lens is 200/2.8 = 71.4mm.
Diameter of the entrance ain't same as pupil.
One of the fallacies.
The diameter of the back of the lens has to be the mount diameter of 54mm which is fixed for all EF and EF-S lenses.
Again one of the fallacies. A rear element can be much wider than the mount, or much narrower than a mount.
So a 200mm f/2.8 lens is going to be pretty well the same size whether it is EF, EF-S, a lens on M4/3 or on a Nikon 1 (1") body. The weight will depend largely on the build quality and optical quality.
Well then why a a 150mm for 4/3" format just is smaller than one for APS-C and for a FF.
Or why a 150mm can be smaller for FF than for a 4/3".
Because it is optical design that can be fitted as wanted by the requirements.
Let me give you a fairly extreme example:
Yes, extreme.
If someone wants to do a smaller and lighter lens with same focal length and F-stop, it is possible but your optical quality can be different, or a usable properties different like minimal focus distance being in tens of meters instead centimetres.
For common designs lenses with same properties are similar by technical standpoint, but they can be bended and changed depending different goals.