Who approves the feature requests made on meta? Is it approved by the SE mods and employees, or is it approved by discussion?
There really isn't such a thing as approving one.
It can get implemented.
The SE team does this.
One of the community managers or the implementing developer will then slap a status-completed onto it.
Essentially, all feature requests are on the radar of SE employees. Which of those get implemented depends on a number of things, most of which are not public. We only hear from them again when the FR is either declined or implemented, or sometimes status-planned or status-review.