Which Component Has the Greatest Affect on Low-Level Listening

Your ears!   @jnorris2005 beat me to it.  Fletcher Munson Curve.

Having said that, clearly some speakers are better at low volumes than others, otherwise Studios wouldn’t have Nearfield, Mid & Full Monitors.

I’ve sold off a long list of speakers & Hifi kit for this very reason.   Thin, lifeless sound at low volume.

I’ve now got a little Bluetooth speaker / DAB radio (Revo) that sounds lovely & rich & full at low volumes.   I can listen to that for hours.   If I want to play at gig levels, I’ve got my main system.

That's an 'effect' silly OP.
The answer is exactly the same as the answer to the same question about normal level listening.  See other string posted yesterday.

In my experience high sensitivity loudspeakers do a good job on low volume. At least my 98dB Ocellia’s do a very good job at low level listening. 

Start with clean power feeding your Amplifier Perhaps a conditioner regenerator or as stable as you can get it into your system. Then as much power as you can supply with your amplifier.
I work from home and 75 % of my listening is low level
High level electronics will make good speakers sound great

Speakers with high sensitivity and paper cones usually sound good at low volume. I own a pair of Tekton Enzo 2.7 which are rated 98 db sensitivity and have 2 8" woofers with paper cones per speaker. Due to an upcoming move, I had to move the speakers into a small room, where I sit about 6 ft away and play at a low level most of the time. They sound good loud, soft or medium. The bass is surprisingly good at very quiet levels even without any eq boost and as long as you’re sitting relatively close. I also used to own Zu speakers which were similar in this regard - again high sens. and paper cones. In my experience, speakers with poly/plastic cones need to be cranked before coming alive.