@Aereus
If you mean the Anger LV of the enemy then yes it's very important.
On the manga isn't obvious who's the narrator but in the novel is very clear from the start that the narrator is Kumo, you're basically reading what is she thinking and for her knowing all the skills of the enemy can decide if she survives another day or die.
She need to know about it bacause that is the core of her strategy, know what your opponent can do and you will have the upperhand on the surprise factor.
The internal monologues are a very big point on almost all Light Novel and also almost always omitted on manga/anime adaptations, on manga most scenes are dialogues or battles but in this plot there's not other choice than use the monologues because of Kumos' situation. Yes, Kumo goes from fight to fight but she needs time to stop and check her new skills and know what new things she can do.
If you have played an MMO/RPG is the same when you level up and check what are your new skills or if a boss killed you because when it's HP is below some point it use a hidden skill or move, on videogames you can die countless times and nothing happens but for Kumo one time is the end for her so she need to know what she can do and what the enemy can do.