prezmulti wrote: Directly overestimates the measurement and through the resistor underestimates the measurement
The use of a resistor and capacitor as long as there is a connection as I think (no diagram, you would paint) amounts to a low pass filter. It's not surprising that it underestimates. I'm surprised it overestimates directly without that filter.
Maybe you have too long wires from the meter to your module. Together with the rather high resistance inside the pullup (I don't remember how many kiloohms, colleagues above stated) the wires pick up interference, or even oscillations occur. Adding
inot wrote: an external resistor of ≈ 2 kΩ
It should help, but I would start with a larger value, such as 4.7k.
prezmulti wrote: do I use an additional resistor with a capacitor ?
no.