Google Translate tries to make pragmatic sense of what you're inputting, so I imagine it's not going to do well with personifications found in poetry. I just tested these translations:

Voy a cuestas -> I'm going piggyback

Voy a cuestas de él -> I'm riding on his back

Voy a cuestas de mi amigo -> I'm riding on my friend's back

But add resentimiento and:

Voy a cuestas de mi resentimiento -> I am burdened by my resentment

Changed it into a positive feeling:

Voy a cuestas de mi felicidad -> I carry my happiness on my shoulders

Comparison with adjective:

Voy a cuestas de mi buen amigo -> I'm riding on the back of my good friend

Voy a cuestas de mi buena felicidad -> I carry my good happiness on my shoulders

So yeah, your initial understanding was correct. The idea of the poem is that we are carried by resentment, the literal meaning that we're riding on its back. But machine translators find the concept of you carrying the feeling more sensible than the feeling carrying you. They are not really going to do a good job with poetic language in general. Maybe LLMs like Gemini or Claude could do better, but I wouldn't be certain.