Most trebuchets throw a distance much longer than their release height, so its not really significant. (Ex: A couple of my throw a distance over 50 times their release height)
Typically difficult to model factors like aerodynamic drag (on the sling and projectile) and projectile spin are actually far more important.
In an ideal friction-less vacuum when throwing on flat ground in uniform gravity, the optimal throw from ground level is at 45 degrees. If your throwing from higher, the optimal angle will be a bit lower.
Assuming you you have a low drag sling (so its less of an issue than projectile drag) you will typically want to throw below 45 degrees anyway, and ideally with top spin. This is because aerodynamic drag on the projectile becomes a large factor for most typical trebuchets sizes and projectiles.
Note that for a particular trebushet, especially a poorly tuned one (ex bad arm ratio, or sling length) you may be able to get far more energy into the projectile throwing at some otherwise horrible angle. Optimal throwing angles in terms of distance for the energy really only come into play once you have a well tuned machine that is getting all the available energy into the projectile.
Its also worth noting that rather extreme machines often have rather strange tuning effects. For example some very large trebushets throwing pumpkins are basically unaffected by projectile weight: their arm speed is not effected by the sling significantly. Thus the arm swings right through where you would want arm stall, and they benefit from longer slings and later releases.
Anyway, release height is almost always going to be a bit less than long arm length + axle height + sling length if the trebuchet is anywhere near well tuned. In an optimal case the arm is nearly stopped at release, and pointing almost vertically, so you can consider the projectile to be going in a circle around the end of the arm, and use a bit of trigonometry to get a more accurate height.
I recommend looking at videos of trebuchets and pausing them at release. Looking at the first two frames after release tell you the angle (and velocity) of the throw and release position. For similar and well tuned trebuchets, the positioning is always nearly the same.