I'm aware I can subtract the mean of the data
That's actually a high-pass filter!
You can see in the time domain output that the filter takes some time to settle.
That is true for any causal system, i.e. any system that can't look into the future; you'll want to read up on "group delay"
Can anyone help with me with what parameters to tweek to have no "settling time"?
I want to minimize that and get similar results as mean subtraction (the plot in orange).
You'll find that if your filter is a linear phase filter, then your group delay is half its length and is constant for all frequencies. That means you can shift its output by half the filter length to the left (i.e. ignore the first filter length/2 output samples), and your two lines will overlap very nicely.
You, however, selected "IIR" as as filter type, and these can't be linear phase filters. There might be some trade-off here, too: non-linear phase filter can have lower delay, but it's not the same delay for all frequency components. I find that whenever you actually want to analyze a signal, that becomes a problem, but that can very well be managed if you can design your filter such that the phase response is appropriate for the frequencies you care about, but that leads to the need for a rather involved filter design. I'm not quite convinced you'd win much by this!