In 2020, what are the most common approaches to power-line-communications for hobbyists? (updated)
very low power system


Either you have very low power consumption requirements, or you have access to mains power. 

I think you're overestimating what a microcontroller needs in power. Modulating information onto a powerline needs way much more power than your microcontroller would need for generation of that data!


  system on a chip safely from mains power. 


Can't exist: Mains power means you need galvanical isolation from anything you might ever touch, and transient protection and the fact that you really need your digital system to have a somewhat stable notion of ground means, this can't be done without a transformer, really. No single system on chip can be a complete powerline modem!


  Has Bluetooth LE (BLE) made the older power-line communications standards old-hat? 


No, because it's something completely different, and fulfills a completely different niche. That's like asking whether airplanes have made tunnel drilling machines obsolete...


  Are there ways of coupling BLE into the power-line that are considered good practices?


Neither. BLE is a 2.4 GHz ISM-band standard, and uses a bandwidth that would be considered very wide in powerline terms, so that you need a very complex equalizing system to work with the powerline channel, even if you could mix things down from 2.4 GHz to 0-1 MHz. The point is that the BLE signal is designed so that it's easy to transmit over the air at 2.4 GHz. That's something very different from being easy to transmit over a powerline channel!

Again, the problems over the air and on the power line are completely different, and that leads to different solution being "easy" or "sensible".


  Surely the world has come a long way since X10. 


Yes, there's multiple low-rate standards for metering and control over powerline.


  The Cypress Semiconductor PSOC 5LP illustrates the class of SOC i'm looking to use as a building block. 


You're solving the easy problem, which is getting analog signal in and out of a microprocessor core. 

The hard problem with powerline is the fact that, unlike an antenna, the impedance of a power line is low (obviously, otherwise power wouldn't reach you), and varies with time, and the channel is terrible. 

So, really, at your point, you need a ready-made modem, including a safe coupler frontend – after all, we're talking lethal voltages here, and you can easily burn down your house with badly constructed thing that you plug directly into your power outlet.