My first few times doing crane work I remember I would feel more comfortable if the operator lowered the cable next to the tree before I hopped on versus out in the middle of the yard where there was nothing within my immediate reach. Or in a bucket / lift and finding myself wanting to stay close to the tree. Same scenario can apply when climbing.
It’s your body’s natural “fight or flight” response to possible danger. There is a psychological aspect to tree work that I don’t think is often talked about and that is that anxiety / fear is very real and for some people it may always be somewhat present. I still sometimes get a little uneasy in certain situations. The key is not allowing it to get to a point that it controls you, hinders your ability to make the right decisions or immobilize you in the tree.
As others have suggested, trusting your gear and in your skills / knowledge is essential. If there are certain situations that make you uncomfortable, doing some rec climbing outside of a job scenario that mimic those situations may help when it’s controlled and you can take things at your own pace as you try to work through it.
Also, another point I want to mention not necessarily in regards to this particular thread but in general and not trying to sound discouraging either, but I think each climber who deals with this needs to be honest with themselves as to whether it’s worth it? If you can’t seem to shake the anxiety even after working on trying to get it to a more manageable level and it impacts your everyday mental health and ability to do the job, then maybe you need to consider a different career or focus on jobs that are more within your comfort range. And there’s literally nothing wrong with doing that. Find your niche in other words.