For me, HRT is purely for the physical changes (and to stop further masculinization).
Thinking of myself as truly a girl came with transition.
After I went full-time but before I started HRT, I was already thinking of myself as a girl by default; even my dreams only ever had me as a girl, in a girl voice.
Thinking like a girl, being able to express my emotions, etc. came about 10 times earlier, looong before I had even heard of the word "transsexual", or any related terms.
It's because I had already decided, relatively early in my life, that I didn't need to think like a guy.
By the time I finished high school, I had already mostly assimilated to my girl friends' minds (I was hanging around with girls 95% of the time already).
So for me, these came about by a change of mindset; none of these required, or were brought about by, HRT, which I only began 11 months after going full-time.
Still, I think it is clear that HRT does have a large psychological effect on many others.
I don't have a problem with simply concluding that it affects some people greatly, and others not so much, or even not at all like for me.