Could be on page 19, the "legal" could've actually meant Lethal.
The RAW says 「法剣」. The 法 is probably from 魔法 (mahou -> magic) and 剣 (ken) is sword. So basically it's just a "magic sword". While this is not a unique way of calling a magic sword, this is more commonly called 魔剣 (maken) instead.
The confusion comes from 法 being used in a lot of law related words. The kanji itself means "law". So I assume that either through AI or due to a lack of vocabulary/kanji knowledge the translator just went with "legal".
The thaumaturgy in the LN and official English translations is just another way to make "magic" sound fancy and distinct. It's not more right or wrong to go with "thaumaturgical sword" or "magic sword". But I'm sure it'll make the people who read those formats appreciate the consistency if the former is used.