Fellow 15-year-old here.
As far as I have read, you would usually implement an Area light by combining multiple things:
A point or directional light at the position for BRDF calculations.
Using the size of the light for a specular highlight.
PCSS or another technique for soft shadows.
[Disclaimer: I'm a hobbyist, not well-read in computer graphics techniques. I may be unfamiliar with common terminology or methods.]
It's possible to explain and reproduce this effect entirely in a “physically-based” manner, simulating the imperfections of physical objects:
Many objects do not emit or reflect single wavelengths of light, but some spectrum, ...
The rendering engine that rendered this image is using a technique called deferred rendering, which first writes scene information (as seen from the camera) to seperate buffers (such as position, normal, and albedo buffers) and then calculates lighting for the image based off this information. It is important that we have position and normal buffers on top ...
In general this is caused by HDR tone mapping. Tonemap curves typically decrease saturation as the input light gets brighter, so that very bright lights are rendered closer to white on the display. If bloom is rendered in HDR (prior to tonemapping) then the bloom around the light can still be highly saturated since it is of a lower intensity than the light ...