Kombucha fermentation time(s)

"Primary fermentation" with SCOBY is really about inoculating the brew. Three days should be enough after which one can remove the SCOBY (kombucha "mother") and use it elsewhere. How long to leave fermenting in the secondary stage is really a question of how much sugar/nutrient has been added, what the ambient temperature is and how sweet/sour one likes one's drink. I prefer to use ginger beer plant now but when I used Kombucha, I left the whole brew (with SCOBY) fermenting for about a week (or so) before straining into a secondary/final bottle. I have not found the addition of some fruit or some flavouring herbs to affect the fermentation time very much - just the taste. Adding some extra "complex" carbohydrates via fruit can add a day to the total but YMMV

The SCOBY is usually a fusion of various organic agents including an Gluconacetobacter, an acetobacter, a lactobacter and a yeast. The sourness develops over time and usually takes a week to get "sour" and is usually too sour after 2 weeks or so at room temperature. The yeast will produce alcohol and CO2, the lacto will mainly produce lactic acid. The acetobacter need the alcohol to produce the acetic acid. So the brew usually get slightly fizzy and slightly sour in the first few days at room temp. The sourness will then increase as acetic acid is produced from the alcohol. That usually happens in days 3-7. For a "normal" tea/sugar base mix the fermentation is mostly over in one week and almost completely over in two weeks. Temperature decrease will cause these timings to increase. Varying the temperature may also affect the flavour subtly.

IMHO absolute minimum time to ferment very partially but usefully is about 3 days. Many would recommend something like 7-10 days. I have never found any use in fermenting beyond 21 days. It is usually quite sour to taste by then. Kombucha brews (without SCOBY mother) can be stored in bottles for some weeks (months even) without ill effect. IIRC the acetic acid is not produced in anaerobioc conditions but the lactobacillius may continue producing lactic acid (and the yeast, alcohol) until the nutrients run out. So the brew will naturally age in the bottle.