the boat situaiton.
If sharing a discharge line woud put a FULL BORE ball valve in each pump discharge, to avoid backflow. (forget check valves, they plug and/or leak too often with dirty fluids like bilge water)

The manual pump will probably preven significant backflow on its own, since it has two check valves in series.

However, the new electrip pump will let the manual pump output backflow freely, if you have no shut off valve.
Effectively, if you install the electric pump without a shut off valve, you have abandoned the manual pump. BAD IDEA

All that said, it is important to realize the having valves in bilge pump lines is an invitation to disaster if confusion regins on board, or people who do not undertand the plumbing well are sailing the boat. Also, it may not be feasible to have manual valves sufficiently accessible in emergency.

An insurance surveyor may reject shared lines.

We ahve separate line on Milvina, despite considerable extra installation work.