Multiple misfires temporarily on cold start

[vonxolo]

2009 528i E60

My car has been doing this rough idle, misfires, for a couple minutes in cold starts.
During this issue the gas pedal is nearly unresponsive. After a couple minutes it just starts to run normal.
I’ve recently replaced the fuel pump, and am pretty sure I need to replaced the filter and sending unit.
Could this be related to the filter? It seems more electrical by its behavior, like the fuel module possibly?
And help appreciated