What is the best modern replacement type for a metalized paper capacitor?

As user EM Fields already suggested, I have already half-answered your question in the linked EE.SE post. Short answer is: get an X2 or Y2 capacitor (see below), these are almost always MKP (metallized polypropylene) film capacitors. Make sure you use a value close or equal to the capacitor it's replacing. Note that both paper and film resistors have very large tolerances (20% is fairly standard over operating conditions), so it doesn't matter if the value is exactly spot-on.

Your application is mains filtering, which is not a precision or high-linearity application. You do not need to worry about the exact type of capacitor. All mains-rated capacitors have similar performance, and performance is basically only dependent on their capacitance value.

What you do need to worry about is that the capacitor is safe to use. If the capacitor is connected between live and neutral, you need to use an X rated capacitor, I recommend X2 to be compliant with 99% of countries' electrical safety regulations. If the capacitor is connected between protective earth (PE) and live or neutral, use Y rated capacitors.

DO NOT use ceramic capacitors. They have very unfavourable failure modes that can cause fire or electric shock hazard.

X and Y capacitors are subject to line spikes, and most will endure multiple small breakdowns over the years as a result of this stress. They fail open because local heating caused by a microscopic dielectric breakdown results in polypropylene melting, which seals off the "edge" of the breakdown.

The practical lifetime is determined more by the number of HV line spikes they absorb rather than by any aging phenomenon.