The Sigma MC11 adapter has no optical elements between the lens and the camera body.
It simply extends the distance the lens is in front of the imaging sensor of the shorter 18mm registration distance Sony E-mount cameras so that the lens is 44mm away from the image sensor. This is the same distance from the imaging sensor as a Canon EF mount lens would be when mounted on a Canon EF mount camera.
Since it contains no optics between the lens and the camera, The MC-11 does not alter the focal length of the lens.
Optically the image circle the lens is projecting onto the sensor should be identical for any specific lens when mounted on either camera.
The difference you are observing mostly comes down to the differences between the two lenses when they are focused at distances shorter than infinity.
Lens focal lengths are measured with the lens focused at infinity. When focused at shorter focus distances, different lenses can behave differently regarding field of view. One notorious example of a lens which expands the angle of view significantly when focused at closer distances is the AF-S Nikkor 70-200mm f/2.8G VR II. Focused at infinity it gives a 200mm angle of view (AoV). It gives a roughly 145mm AoV when set to 200mm and focused at the lens' minimum focus distance (MFD). In contrast, the competing Canon EF 70-200mm f/2.8 L IS II gives an approximately 195mm AoV at a similar MFD.
Focal lengths, particularly with zoom lenses, are approximated to the nearest "standard" number. You'll almost never see a lens marked as a 242mm or 246mm lens, even if that is their actual focal length. They'll both be sold as 250mm lenses. Lens makers tend to almost always round "up" on the long end and "down" on the wide angle end.
In the case of a lens such as the Sigma 18-300mm, which has a long end that is 16.7X longer than the wide end of the focal length range, certain compromises are made to fit such a wide range of focal lengths into a single zoom lens. This almost certainly includes focus breathing that causes the AoV to get wider as the lens is focused closer than infinity. It also includes a little exaggeration of the lens' actual focal lengths, even when focused at infinity.
However, the similar Sigma 18-250mm f/3.5-6.3 DC OS HSM in the Canon EF mount tests right at 18mm (18.53mm in the center of the frame to 17.9mm in the corners of a FF sensor) on the wide end and 250mm (247.9mm in the center and 257.9mm at the corners) on the long end according to DxO Mark¹. One the other hand, the Sony E-mount 55-210mm f/4.5-6.3 OSS is measured at 202mm in the center of the frame and 205.6mm in the corners when set to 210mm. So at infinity the Sony 55-210mm lens actually fudges more than the Sigma 18-250mm does!
DxO does not test the Sigma 18-300mm f/3.5-6.3 DC Macro HSM in the Canon EF mount, but they did test it in the Pentax KAF mount. That lens measured 281.5mm in the center of the field and 286.3mm at the edge when focused at infinity at the longest focal length. It ranges from 18.9mm in the center to 18.1mm at the edge when focused at infinity at the widest angle.
¹ Please select 'Measurements → Distortion → Profiles' and the appropriate focal lengths for each lens to see the actual focal length measured at various points across the lens' field. The left side of the graph shows measurements made at the center of the image projected by the lens, the right side of the graph shows the measurements made near the edge of the lens' image circle, which would only be visible in the corners of a rectangular APS-C sensor (all three lenses were tested using APS-C cameras). The intervening points on the graph show measurements taken at various points between the center and edge of the lens' image circle. The corners of 1.5X APS-C sensors, such as the Sony α6500 and Pentax K5IIs, would be slightly further away from the center of the sensor than the corner of a 1.6X APS-C sensor as is found on Canon's APS-C cameras.