Here is some information about how head units are built, what those amplifiers look like, and how they are configured.
Head units use a small amplifier IC (integrated circuit) to power speakers. This chip is about the size of a quarter, in total. Consider the size of an entire aftermarket amplifier and you get an idea of what expectations you should have for this tiny circuit.
For example, the picture below is of a pretty standard amplifier IC in a Pioneer-made head unit. It would have ratings similar to that of your Sony. In this picture, you see the IC removed because I was making some modifications, which aren't important to this discussion. That IC does ALL of the speaker amplification for all four channels.
Next, consider the topology of the amplifier IC. It already has bridged/balanced outputs, meaning there is signal on both the + and - wire. You can think of the amplifier IC like an 8 channel amp that has already been bridged down to 4 channels. For this reason, it is not possible to bridge a head unit any further.
Lastly, the typical rating method of IC amplifiers (used in home or car audio) is if one channel can produce rated power for one second, they can label the IC as having the capability of producing that power into any of the four channels - even if that isn't simultaneous. Meaning your head unit can, in theory and in the right conditions, product a signal equivalent to 52W into one 4 ohm load for one second. That may not be pleasant to listen to (given distortion) but it can make it happen. Part of the problem with simultaneous power output (such as all four channels simultaneously) is power supply requirements. Consider the current required to produce the rated 216 total watts the amplifier IC is rated for, then consider the size of the traces in the amp. You'd quickly realize the traces would melt and/or catch on fire if asked to supply that much current. As such, the actual total power output of all channels simultaneously is about the amount of one channel. in your case, that is 52W divided by 4 which is about 13W per channel. Even then, distortion is high, so the typical usable (i.e. pleasant to listen to) is about 5W per channel.
So why can a head unit seemingly get "loud" on speakers? Part of that relates to the sensitivity of smaller, cheaper speakers. Those lightweight cones move more easily and with sensitivities near 90dB at 1W @ 1M means that at the listening position you could achieve around 100dBA per speaker. That will seem pretty loud in a vehicle with the windows up, even if it doesn't sound very good because the amplifier distortion is high and the speakers are inexpensive or not ideally mounted.