Alright, set everything up again and tested the flow meter directly on the level shifted input. It works better and exactly like I thought:
The flow meter sensor line is pulled up with a resistor, that gets pulled down by a kind of FET when it does not detect a magnetic field.
My level shifted line is basically a pulled up line with two 10k resistors, one to 3.3V and 5V each, as mentioned
before. When I connect that to the Flow meter the signal line gets pulled down to something like 1.2-1.7V. Maybe that's due to wire and contact resistance limiting the pull-down over the contacts and long wire connecting my circuit with the flow sensor.
I'll try to measure and reduce contact resistance. Another funny thing: when I measure the voltage with a voltmeter, the moment of contact creates enough voltage drop to be registered by the PI as LOW and consequently leads to some flow being registered. So maybe I just need to add some 20k pull-down resistor and the flow will register fine.
Ultimately I may just go down the route
@robsworld78 suggested: simply use a GPIO pin and drop the 5V to 3.3V using a resistor bridge ^^