> For the branch of trading technical analysis which assumes that all information is factored into price and price action, the variables will drastically be reduced probably to something like volume, low, high, open, close etc.
I'd call that quantitative analysis, not technical analysis. The difference between them being the difference between astronomy and astrology. Technical analysis refers to classic trading strategies of visual patterns in the price charts like double top or bottom, head and shoulders, etc; these patterns and their traders suffer from massive hindsight bias. Feeding prices into computers looking for patterns is not technical analysis unless you've programmed the computer to look for said human found patterns. If the computer is actually searching for real patterns and you're testing them properly with forward tests on fresh data, you're doing quantitative analysis not technical analysis.
TA is practiced by manual traders, Quants are generally automated traders or traders doing proper statistics rather than relying on the visual patterns manual traders think they see.