Electronic – Implementing powerline communication on a battery-fed 12V line

• What interface you need to line depends on the specific power line modem.

  Some will have the interface built in so that you can connect phase and neutral directly, while others may require an isolation interface.

  The manufacturer of your modem should provide very very very clear documentation of what is required.

You will usually only be connecting to one phase so have to deal with Phase to Neutral voltage.

If a coupling capacitor was needed I would use one with full "X1" certification.
X2 is of lower spec than X1 but still tested.
X3 is lower spec than X2 and is untested.

It's likely that the value of the users lives, your life and the equipment used is far higher than the cost of a top rated capacitor.

Xx capacitors:

This EPCOS document provides valuable information about X rated capacitors

Some useful related information here Line filter capacitors
They note:

Class X is for applications where failure could not lead to electric shock (hot to neutral).

Class X1 capacitors are intended to operate safely even in the presence of spikes on the mains supply of up to 4 kV (installation category 3 or overvoltage category 3 according to IEC60664), which are normally industrial supplies, but some standards call up class X1 capacitors if they are connected directly to the mains supply upstream of the equipment fuse, irrespective of the type of mains supply.

Class X2 capacitors are intended to operate safely even in the presence of spikes on the mains supply of up to 2.5 kV (installation category 2 or overvoltage category 2 according to IEC60060), which are normally residential, commercial and light industrial supplies.

X capacitors can be found from 0.001 uF to at least 10 uF and are only made in film.

And

Classes X1, X2, and Y were originally defined by the IEC in IEC 60384-14. CENELEC has adopted EN 132400 (technically equivalent to, but structurally different from IEC 384-14 2nd edition), which now defines seven classes of line-filter capacitors.

Class X1 capacitors are impulse tested to 4 kV (higher for capacitors over 1.0 uF).

Class X2 capacitors are impulse tested to 2.5 kV (higher for capacitors over 1.0 uF).

Other - not suitable:

Class Y1 capacitors are impulse tested to 8 kV, and Class Y2 are impulse tested to 5 kV.
Classes X3, Y3, and Y4 are for lower-voltage capacitors, none of which are presently called up in safety standards.
Other impulse tests also apply. These include a 1000 hour endurance test during which the capacitor is subjected to a continuous overvoltage condition, plus periodic 1000 VAC spikes, and a flammability test during which the capacitor is hit with a series of transients while under rated voltage. Capacitors conforming to IEC60384-14 normally also conform to EN132400, and vice versa, and should be accepted in all European countries.

For a reduction in data rate due to interference that is as slight as that shown in your table you are very unlikely to see any deterioration of the spectrum whatsoever.

I am wondering what would be a good way to quantify this effect.

Do exactly what you did in the table - plot the effective data rate when an appliance is on compared to when it is off - the table tells you a lot so well done on that - it's useful to see. You could presume that the effective data rate reduction is due to packet retransmission due to packet corruptions. You could also assume that when data rates are higher, the packet length is shortened in order to make retries of smaller packets more liable to be received correctly - this also reduces overall data rate bearing in mind that the reduction would be greater if the packet length were kept bigger because of the probability of errors due to longer packets.