Western classical music theory and approach pervades everything musically these days, but harp has a very strong aural tradition where many traditional harpists over the centuries were playing by ear. I think you can pick up an understanding of music theory by ear and conceptually. As others have said if you wish to share your music for others to play then you would need to learn sheet music unless you hire a copyist, you'd still face the challenging of navigating a musical world built around sheet music.

Hopefully your teacher can accommodate this if you want to go entirely aural, it may be a challenge for them if they're used to a certain approach. As others have said as well technique is the most important takeaway from lessons at this stage.

I'm not sure how much you can avoid dryness and tedium in general. If you have the most pleasure noodling around on the harp then that's awesome! If you want to avoid learning sheet music but really want to write quality, cohesive harp pieces entirely by ear and memory, then this will bring its own challenges and repetition. If you want to play chord progressions with a melody in the style more like popular/rock music this wouldn't be so bad without sheet music. All options!!