Where and why are style tags removed in the render process?
To complete Clive answer, you could directly use your $fieldRenderable variable into a new renderable array that you will return from your build() function.

Example (not tested) :

$build = [];
foreach ($fieldsToRender as $field_name) {
  // Do your stuff
  $build[] = $fieldRenderable; // you can put whatever you want for the key
}
return $build;


The render process is done when you return the $build variable.