How the label is assigned
Mula is the 19th of 27 equal nakshatras. Its interval begins at 240°00′ and ends just before 253°20′ of the sidereal zodiac. A planet or ascendant in that interval receives this label.
Each nakshatra is 13°20′ wide and contains four padas of 3°20′. The pada is calculated from the same sidereal longitude. No language model is needed to assign it.
How to use this reference
The traditional lord sequence gives Ketu for Mula. This is a classification within the chosen system, not a physical property of the sky.
Compare exact degrees and ayanamsa settings before concluding that a different tool is wrong. A position very close to a boundary can receive a neighboring label under a different method.