How can I restore the shine to a quartz countertop?
Do not use sealer on engineered stone, it has to be mechanically re-polished if it's lost its luster due to abrasion. If you're lucky it's just dirty.

Of course, you cannot apply a sealer to Silestone quartz countertops, so it's just a matter of cleaning it. –countertopspecialty.com



Do not use oil-based soaps for this. Dulling of the shine occurs because of residue left behind on the countertop. Oil-based soaps are often used on porous surfaces because they are designed to soak in, not to be completely removed. Standard dish soap is best. [...]
To remove cooking film from the quartz, spray the space with window cleaner. [...]
Avoid Using More Polish. Quartz countertops are polished within the manufacturing company, using a sealing surface polish. Further polish added to the top will only create excess buildup which will further the dull look.
–How to Polish a Quartz Countertop to Make it Shine, doityourself.com