i still feel anxiety, and no, it's not pleasant, but to me it's like having a headache, it's there, you know it, but you get on with your day. And it goes away at some point or another.
I have yet to see a performer about to perform some major work and not feel the slightest "hum" of adrenaline. The fact that you face the unknown alone will set up an instinctive brain reaction. Probably goes back to cave men about to go hunting or something.
For me it got better the day i thought " LAdies and Gentlemen, this is me , me thinking, my emotions, my abilities and limitations . I can not be more than that at the moment, this is all i can be, this is what i can do. "
And then you go on stage, and you start. Thinking about the 1st note first is usually a good idea. Then you move on to the 2nd one..

And i'll play as good as i practiced ( not how much, but how well i worked) and as good as i can concentrate and create the fusion between body, mind, instrument, feelings and flow of the music.