You could look at it the other way round? Instead of anxiety preventing your breath hold, learning to hold could become part of the solution to your anxiety?
I've been very anxious, from being a small child, and was depressed for many years. It really messes up my climbing. I get stressed and scared, stop breathing, hold on too tight, muscles fatigue and then I fall
Or I push past the hard move and pull a big breath in and realise I was all tensed up, and not breathing! Training breathholding can be a great way of discovering the process of how stress responses can throw you off in life, in a safe environment.
For your breath hold, purely from an anxiety point of view, I'd say take all the pressure off. Don't even time it, and just focus on the sensations you have when holding; in your body, mind, emotionally. Most of all, smile!!! Smiling is the most powerful mental health medication in the world! Just let things happen, observe. And you'll learn the difference between an anxious response to not breathing and calmly going into it. Then as you become more aware of positive and negative responses, you can choose the positive ones. And then it gets easier. You can use that in general life as well as breath training.
I've found that anxiety pulls me up into the conscious layers of my mind, worrying. (Where panic about not breathing ends a breath hold early.) And this is where all the counselling and therapy stuff works too, challenging negative thoughts etc. But after many years of therapy, meditation, breath work and so on, I'm learning that, for me, there's an order to things:
An unconcious anxious thought happens, undetectable. Then a physical sensation in my body comes on a fraction of a second before the emotional response, and then the conscious thinking starts to amplify it all. But breathholding is an excellent way to learn the physical sensations associated with the anxiety response. And that allows you to cut it off before it triggers the emotional and conscious thinking amplification cycle. If you learn to do that, and stay with the positive response, smile at it to make it stronger, negativity or anxiety kinda bounce off, and your breath hold will become easier.
And you can do the same with anxiety in everyday life, too
)