Technique extinguishment what? Why are we acting like Hana didn't use a low output JL to neutralize the big bird Nue? TE is.....

...TE is just the name of the technique, the move is Jacob's ladder itself, it's like saying Sukuna can use shrine, well duh! He can use shrine in the form of dismantle and cleave and furnace,

It also makes sense since Hana is still doubtful at this point if they should hit megumi or not, we can also clearly see the low powered stream of light hitting Sukuna, i think it makes little sense if she can use TE and didn't use it at the very end.