In part I agree with Torkel. For many amethysts were a jewel for part mourning. Queen Victoria was in perpetual mourning after the death of Prince Albert, so, when she wore her mother's amethysts, little significance can be attached to that. Her mother, Victoria, Duchess of Kent, definitely wore her amethysts at times when she wasn't in mourning, possibly because they were her most significant jewels.
In the case of Queen Alexandra, I suspect that we are looking at another scenario again.
The first reports of Queen Alexandra wearing amethysts (as her principal jewellery) come from 1904. Prior to that she wore either jet for early mourning or diamonds and pearls for half mourning. We know that shades of mauve and violet were her favourite colours. And, according to the press reports, she wore a mauve dress for the gala at the Opera in Berlin in 1909.
The first reports of Queen Alexandra wearing the amethyst necklace and tiara come from the wedding of Princess Alice of Albany who married on 10 February 1904.
Was the Queen in half mourning then? I don't know. Does anyone?
Below is a description of HM's dress and jewels at the wedding.
There are reports of Queen Alexandra wearing the jewels for "routine" evening Courts with little evidence that the Court or the Queen, personally, was in half mourning. For example --
The 2nd court in May 1904
I doubt if Alexandra was in half mourning for the ball given by the Duchess of Wellington at Apsley House in 1905 when the Queen also wore her amethysts.
1905 Apsley House ball
Having given those examples, I admit I could be very much on the wrong track, especially as I haven't tried to ascertain when Queen Alexandra would have been in half mourning.
Did Queen Alexandra wear the amethysts in Berlin? The only evidence (and I admit it is flimsy) is the sketch.
Queen Alexandra was at the banquet, and according to protocol HM would have been seated next to the Emperor, so I suspect that the person depicted was meant to be Alexandra. But, I could be mistaken.
I find Alexandra's use of her amethysts interesting. It is a great shame that we don't have any photos of her at the events where she was reported as wearing the jewels.