Your outlet takes a snap on wall plate. Make sure the circuit is off before you work on that outlet.

Or, use a regular Decora-style plate - it's screws go into those little threaded holes at the extreme ends of the outlet.

It looks to me that the opening is too wide (top to bottom in your picture) and maybe too long. An oversized plate (Google "jumbo plate covers" for suggestions) will cover the gaps but a plate alone will not give adequate support for a receptacle that doesn't reach the box that is supposed to support it. A box extender may be helpful.

Or outlet spacers work well too.

Yes, the supplied screws may not be long enough, but just get longer ones and use either a box extender or appropriate spacer. Once you get the receptacle firmly attached with the mounting tabs on the surface of the backsplash, you might find that the short plate-mounting screws are too long because they hit the backsplash behind the threaded hole(s). You might have to drill into the quartz to provide some extra clearance. Or shorten the screws.

Hi! how did you end up fixing this? im havifn the same issue with my full height quartz backsplash.