Habits do have a lot to do with it, both in how you feel stuck in the old, and how you get to the new. It gets better. I came to think of it as two forms of "other:" one private and personal, one public. I think the disbelief is part worrying about how you are seen because you are not sure how to measure it, and feeling overwhelmed in the day to day expectations. It stops being new quickly. You have to get over "othering" yourself before others can entirely.
For me, I felt trapped labelled "trans" and not female, even if I felt female and looked it. Some of the problem was lack of confidence, no matter what anyone said about how I looked. I had a notion about how I wanted to be seen, and had no idea if I was anywhere close to it. One grows into an identity in life, reinforced by daily interaction with others. You are messing about with that in all sorts of ways, mostly good, reshaping it in an amazing brief time. Generally, you really don't now what it is you are doing or how, you just do. Some of it is passive or internalizing. Growing up, you take all sorts of hints from others about where you fit in and how you look compared to others, especially through puberty. You are taking all that and compressing it into a few years, but without the schoolyard games and cliques.
It took a while before I saw "woman" in the mirror even after FFS. But it DOES happen. I found that it partly takes developing a new set of habits in your daily life, either intentionally or by necessity. That's completely you and yourself alone, it's not part of your interactions with the world. For example, HAVING to do all the maintenance that other women do quickly stops being unusual in your mind and becomes a necessary chore. You are no longer "different" when you are confronted with a face in the mirror that needs "enhancing" like any other woman. You figure out how, and it works, and you walk out the door. Sometimes looking at models and celebrities without makeup reminds you that most of what you think sets you apart as T isn't really true. They look just as dreadful. You figure out what your expression of yourself is, and you develop a routine around that. You also learn to do it with as little bother as possible. You stop "othering" yourself. You pass as you, not some other woman, which is the point I suppose and was true all along. You are setting you free again. It's not so much being confident (but you want that anyway in life) it's about being comfortable in your skin to the point it's just your skin again. Normalcy.
At the same time, the way my transition evolved didn't help erase my sense of "other" regarding the rest of humanity (or the ones I interacted with) and my anxiety about fitting in. I had a very public transition locally. I was older and fairly well known in my community. People knew, and 99% of the time it wasn't an issue (I have one neighbour who still refuses to use the correct pronoun after three years, but that's about the only one who is malicious). Life went on as before. However, that meant that there was not a lot of stealth and it was twice as hard as I had to be "on my game" all the time. It wasn't as bad as schoolyard pecking orders, but I felt under the microscope for a while. I knew women were watching me to see if I knew what I was doing from makeup to clothes -- which they do anyway to other women. The men had to rethink how they interacted because others were watching THEM as well as me, and they were insecure. It also meant that at the start, there was some ongoing curiosity and I could be sure if I met someone in a social situation, especially a man, someone else would say: "did you know about her?" I didn't stick out particularly, as I am pretty together, it was just local people wanting to gossip. It was hurtful, especially if someone flirted with me in front of others and then heard more about me later. Sometimes it made the transition hard to forget. And I really wanted to forget. In time, it all became background. Since so many knew me before, pronouns still slip time to time, but that's the price of knowing people 20 years or so and being involved. It was hard to shed the "T" internally when you could not escape externally, even if you passed well. But that wore off as I was no longer a novelty and people got used to seeing me as female. Their reality was me as I am, not as I was. That reinforces your confidence. Oddly, when I first noticed being discriminated against, it wasn't as T it was as F.
During that time, when I was in places no one knew me, I was acutely aware I was testing myself. I really felt the same dialogue of doubt you describe. I was on my guard, worried about my voice, and worried about eye contact. All three are killers. A lot of it is just shedding the idea of being "different." If you act as if you are different, then others pick up on that. Don't. You set that tone. Eventually, you refine and fall into a routine that works effortlessly just like your maintenance, which is your new norm 24/7. Where once you walk through an airport convinced everyone notices you and clocks you, you end up being part of the crowd, another woman on her way to somewhere else just crossing paths and only getting noticed because of what you are wearing, or because you just catch an eye (good notice!). I think you go from worrying about being noticed for the wrong reasons to wondering if you are really THAT plain. There are people here who say, just let go and be, I think that's exactly right. If you are natural and everyday about it all, no one else thinks otherwise. That said, it's not an overnight event.
I did find that for those I knew before transition, I had to put them at ease by reaching out as normally as I could. They don't know what to do or if they SHOULD do anything. They don't know if they should congratulate, compliment, or ignore what you have gone through. For some, it's a lot like trying to figure out how to acknowledge a death -- what's the right thing to do and will I hurt their feelings? Sometimes they just don't say anything as the least problematic path. The women at least know the language of compliments -- and it's like exchanging symbolic ceremonial gifts as you reciprocate. The men are trapped between panic (I don't want to look like I am flirting!) and awkward almost compliments (I'd never know! You do it so well!) All I can say is smile and accept in the spirit offered. Then resume being as typical and normal as the next woman at the party.
While still worrying about the voice, that is...
