The calculation you make by hand is consistent in the hyptohesis of a beam on 2 supports. At the extremities, the normal rotation in the plane is free.
If the ends are recessed, the stress and deflection will necessarily be lower. Now I don't have the formula in mind anymore but the SW result is not necessarily inconsistent.
Personally, I have never managed to master the calculation in beam or shell under SW.
The good old volume calculation works in 95% of cases (unless you are on a framework or with very large length/section ratios). The interest of the volume is that at least you have an idea of what happens at the junctions and embeddedness (which are the critical points usually). So it's sure that you get a fair of knots/elements but with modern PCs generally you get a result in less than 5 min.
Try to do the math on your piece in volume, it should be okay (although you're a bit long).
Your result seems to correspond to the case where your end points are fixed and with a central joint (if the ends of the beam can't get closer to the center, it necessarily reduces your arrow to the center). In beam I don't even know if you can simulate the flat support of your beam at the two ends.