Language is not thought, and thought is not language. One of the tenets of mindfulness meditation and cognitive behaviourial therapy is that: you are not your thoughts. I am not a trained linguist, but I see language as a vessel for our thoughts.

But I think the relationship between language and thought is one that is frequently discussed. Think Orwell's 1984 - the idea that language can constraint thought. I think this Wikipedia article does a better job than I will be able to: https://en.m.wikipedia.org/wiki/Language_and_thought

What if the surgery is not a matter of life and death? Something less severe but that still has important implications wrt personal identity?

One example I can think of is MTF/FTM transitions. I am not sure what the politically correct term is here, so please forgive me. Neither am I a medical professional, so I'm not too sure on the intricacies behind it.

M/F go through different physical changes during puberty, and I imagine some of those effects will be irreversible past a certain age. Should the child be able to decide if they want to have such a surgery / medical procedure?