We move thick, fibrous stuff in pharma waste lines, and the pump question comes up there too.
Real immersion PD pumps are rare. The one type that can sit in the liquid is an air-operated double-diaphragm pump (AODD). It runs on compressed air, has no electrics in the pit, tolerates solids and runs dry without damage. With stainless or ductile iron body and flap valves (not balls) it handles fibrous slurry well. You need a compressor and the flow pulses, so put a pulsation dampener before the separator if it minds.
The other honest options keep the pump dry:
A progressive cavity pump next to the pit, below its lowest level, with a short flooded suction and a macerator in front for the straw. That’s the classic separator feed and gives the steadiest flow. A hose (peristaltic) pump, which can self-prime several metres and doesn’t care about fibres, at the cost of hose changes.
For the screen: the core set only has a Motor pump, but the Process library has Diaphragm pump, Peristaltic pump, Gear pump and Submersible pump, and the Wastewater library has a Screw pump (closest look to a progressive cavity) and a Dosing pump, if your organisation has those libraries. Pump symbols take Running, Speed and Direction values plus the hand/auto Mode badge, so bind Running to something like pump_running and Speed to the VFD’s output in percent. If the device sends keys named after the symbol id (p1.running, p1.speed), they connect by name without picking.