Exception No. 2 to (3): A single outlet
receptacle supplied by dedicated branch circuit
which is located and identified for specific use
by a sewage lift pump.
Yes, but if by "permanently installed" you mean it is HARD WIRED and not plugged into a receptacle, then the rules for GFCIs no longer apply, unless the "sump" is big enough to be called a "swimming pool or spa" (680.21.C) or your residence can be classified, as mine likely can, as a "circus or carnival" (525.23 (2)).
Any marketed for residential or other light duty are usually going to be cord and plug connected, and have integral controller such as a float type switch.I have never seen a direct wired sump pump but I am not surprised if there is one out there