What is the medical term for semi-mindless activities to help reduce anxiety? ... such as gardening, mowing, cleaning... perhaps driving What is the medical term for semi-mindless activities to help reduce anxiety? ... such as gardening, mowing, cleaning... perhaps driving.

I recall that, maybe, the word asynchronous was part of the term * which based on present answers now seems less likely * .
I have not been able to find any term, medical or non-medical, which includes the word asynchronous, but to add to the answer by @user20460 there is the non-medical term hobbies.
Taking part in hobbies and other interests is recommended to anyone who suffers from anxiety and/or depression because not only can it provide a distraction, but it can also alleviate boredom which in itself can create or exacerbate anxiety - see also, Csikszentmihalyi (2000).
As NoPanic.org points out, you should...

do something that makes you happy. Every day should include a bit of ‘ME’ time. It may be losing yourself in a book, playing or listening to music or a self-pamper session. However busy life seems, you deserve that special time.

References
Csikszentmihalyi, M. (2000). Beyond boredom and anxiety (Vol. 721). San Francisco: Jossey-Bass.