Can I caulk the corner between stone countertop and stone backsplash?
Some general input here as I install granite counters weekly.

No way the granite is bound to each other
trim piece probably has silicone (I hope) binding it to the wall
you don't have to have silicone on dry areas.   If someone spills a cup of soda on that counter, some will seep behind trim but it is pretty minimal (I have tested for fun).   The trim piece is cut with laser and the top of counter is sanded flat so these pieces while somewhat pourous are pretty water tight... but all it takes is a small divot and liquid pours in... and obviously this widely varies on type of granite.   Yours is darker and has lower veins so I would guess it is pretty water tight.
but it would be normal during install to caulk there.   I am not sure what the other guys are on here suggesting white or colors.   All kitchens and baths get clear silicone - that's it.   White, grey, black, whatever... it stains and colors fade in spots over time.   Clear will last the longest and almost impossible to stain.
make your silicone as thin as possible to cover the crack.   If you go up 1/4&quot; and out a 1/4&quot; and have a huge bead of caulk, even if it looks good it won't last as long as every time you wipe the counters you will put pressure on it.   If you can barely see the caulk that is optimal.