Those sparkles are caustics (light bouncing off a glossy surface onto a diffuse surface), which are still really hard for path tracers.
The default render settings are also tuned to make them even less likely, sacrificing physical accuracy for lower noise and reduced fireflies (caustics being a common source of fireflies)—compare the default Filter Glossy 1, Indirect Clamp 10, path guiding off
Note the extra noise & fireflies, though. Even at 8192 samples (1h 15min), whole parts of the image are still unusable. And path guiding is only available on CPU, so you really pay for each one of those samples.
or adjusting the shader to be highly emissive when the incoming ray is very very close to the normal direction (basically the same thing as the area lights, but done in the shader instead):
I think that “fake it” is the right idea. Also, be sure that the ball is illuminated from several different spotlights of various colors which surround the top of the ball.
Basically, the “reflection” in the third image is plausible, and in this case that’s really what counts. (But it usually would be “multi-color.”) Find any cheap way to get: “good enough for peace work,” and be done.
Why do you assume this… ???
…also there are two render engines:
EEVEE
Cycles
For (so called) realtime renderer (sometimes online renderer) like EEVEE bouncing light is not cheap so they restric the bouncing by default… you might increase the value for you scene.
Why do you think Cycles is called PBR (physical based renderer/ also offline renderer) ??
Also there are two setups for viewport and final render… (and of course the material preview… with very basic lights…)