Nice take on the theme! I like the visual style of the game. The tutorial level at the beginning is well executed, introducing the main mechanics without interrupting the gameplay. The music and sound effects complement the gameplay really well.
You've managed to create a truly cohesive experience, and the gameplay is addictive as well.
One suggestion if you decide to continue working on it after the jam: consider adding some visual feedback when hitting zombies—some pushback or a change in sprite color to indicate damage. Adding some extra game juice like screen shakes could also enhance the experience.
Overall, awesome job! Keep up the great work!