I drink kombucha, a fermented and very slightly alcoholic tea, in order to ease recurring gastrointestinal distress. Although I use this drink as a tool, is it considered a breach of the fifth precept?
The purpose of that precept is to prevent loss of heedfulness through intoxication.
If your reason to drink tea of some kind with very little alcohol in it, is for medicinal purposes, and if it does not cause the loss of heedfulness through intoxication, then there is no violation of the precept in my opinion.
Buddhist morality, as a rule of thumb, has to do with how such actions affect your ability to practice (i.e. can you still meditate), and does it cause suffering in yourself or others, as opposed to morality being based in compliance with the demands of a supernatural being.
So, on those grounds, this amount of alcohol is not problematic. It won't make you behave in a way that makes you break the rest of the precepts.
As for how much Kombucha you'd need to drink to get smashed and risk breaking the rest of the precepts...you'll start puking and farting before you get drunk on Kombuch, this guy tried it.
...almost a gallon of noxious fermented tea just to break a blood alcohol level of 0.01
Would really depend upon which school of thought you follow, and at that, which lineage. Some are as strict as to say that definitely yes, not permitted. Then there are most others that are more mainstream or even liberal in the interpretation of Buddha’s teachings. The question I would ask myself is - is there any other source that I can use without alcohol, and go from there. This, only if you are especially conservative in your approach to the precepts.
If you do continue to consume Kombucha, perhaps consider switching to one with a lower alcohol content. They do vary among brands, sometimes widely. The bottle that I am looking at now states .5% by Vol, but I’ve seen both higher and lower amounts in other products. Please also consider the caffeine content if you are sensitive.