you don't have an lsd - the psm is electronic (uses the abs to control traction).
the boxster uses a 'transaxle' which is a combined transmission and differential - flushing as per the pelican how-to does both. you will need 3 litres of fluid.
https://www.pelicanparts.com/techarticles/Boxster_Tech/38-TRANS-Manual_Fluid/38-TRANS-Manual_Fluid.htm
note pelican will also sell you the fluid ...
and pro tip - take out the fill plug first. you brick your car if you drain the fluid only to find out you can't get the fill plug out.
otherwise pretty much everyone will tell you to use the porsche fluid. i've used a variety of 75w90 fluids including motul and redline with no issues. if you want to do more searching, the porsche 996 uses the same 6-speed transmission and a lot more info out there for the 996. i think you'll find that the gl-4/gl-5 discussion is a bit moot since most of the high-end gl-5 gear oils have been engineered to no longer corrode the yellow metals in the transmission.