The crystallizing to gems have wrong names on a few. Sapphire recipe is named emerald and so on.

I noticed this too, using the "whats it used for" mod. I have to put in sapphire to get topaz to show up in the search.

Confirming this bug, though it seems to potentially be coming from ShinyBob.

Crystallization from crystal seedling and crystal catalyst yields the wrong products for 4 of the 6 recipes (amethyst ore and diamond ore yield the correct products).

Incorrect products:

Crystallizing topaz ore -> emerald ore
Crystallizing emerald ore -> sapphire ore
Crystallizing sapphire ore -> ruby ore
Crystallizing ruby ore -> topaz ore

First few lines of ShinyBob's locale\en\bobsplates.cfg:

[item-name]
ruby-ore=        Topaz Ore      
ruby-3=      Raw Topaz      
ruby-4=      Cut Topaz      
ruby-5=      Polished Topaz 

The rest of the definitions match the patterns listed above.

In-game results: https://imgur.com/a/YxuxB

The Shinybob Author made some tweaks to gems so the colors match the tiers
yellow-red-blue-green-purple (or was it purple-green)

I see... an interesting hack. Unfortunately, it seems something got lost in translation with the crystallizing recipes, as can be seen in the imgur album (compare recipe on crystallizer vs output product).

Reported in ShinyBob as well: https://mods.factorio.com/mods/Inequalitix/ShinyBob/discussion/10300