Brake pad play – is this amount normal once the pin and bolt are installed?

Yes

I recently shifted to hydraulic disc brake and this was my first question to the LBS after the test ride.

519% normal.

not 520%.
not 518%.

definitely 519% normal.

But if the sound of rattling bothers you, take out the stainless steel spring and stretch it outward to push the pads harder to the caliper.