The words themselves are weird, and the connotations attached to them are understood differently by different people. I think that's part of why we can't agree (or else, some actually don't want to agree) on any of this.

1. Gender, some people think it means sex. When you take it to mean biology, that sounds like the part that needs to be addressed. If you take it to mean a social construct, well then it's more about expectations & stereotypes. Those can be addressed with therapy, instead of starting with physical interventions.

2. Dysphoria, just means an unhappiness, a malaise, or literally a dis-ease. (The opposite of euphoria.) So if someone is unsettled with the reality of their own body, that is by definition an unhealthy state of mind—and should be treated as such. Cult activists would argue for a different meaning, and want to see dysphoria de-classified as a mental health condition.

are there cases of therapy for gender disphoria that made trans people fell worse than just transitioning?

This is exactly the right question. Personally, I would never say just transitioning since that is such an invasive approach. It would be impossible to prove this within one individual, but there were studies that showed no benefit from transitioning. Unsurprisingly, these were withheld from publishing until they were forced to by the British courts.

https://www.transgendertrend.com/the-tavistocks-experiment-with-puberty-blockers-part-5-the-belated-results/

If we can show there is no benefit, then it logically follows there can only be harm—from the countless false-positives that will inevitably come up after the current trend among children and young adults gets old.