Full Stop.

Yes, monster hp is higher since it is expected in a rhythm game for a player to hit >50% of notes + the equipment further tips the scales in the player's favor.

Some pointers for this particular combat and just in general:

1. It really matters when you hit the note. E.g. if you hit a shield note dead-center you can completely negate the attack whilst hitting only a side results in you only partially blocking the attack and still taking damage. Try to line up the horizontal lines of the notes with the play zone. (See one of the screenshots for the exact timing.)
2. Expanding on that, the stick can actually be a better weapon against the rats due to their low attack, allowing you to heal all of your lost hp in successful combos if you miss some block notes.

Hope this helps!

Would you mind sharing a video of you playing the game? Just to make sure you are not facing a bug.
Or maybe difficulty does need to be optimized. After all we have been practicing the game for a month and can't really judge it fairly. But seeing someone else play it will help greatly.

That said try the very first rat. Its rhythm pattern is the simplest and 1000hp should let you practice the game. If you missed the stick item, it is in the crime scene near the start of the game.