What caused "excess liquidity" in equity market, when CPI was deflationary at the same time period, which caused 'market crash in 1929' in USA?
The inflation data provided are not useful in this context. The average inflation shown is a mixture of the outcome of a post-WWI deflation, recovery, and price stability. One would need to look at more specific periods. FRED CPI data

Equity prices are supposed to equal the discounted value of future earnings/dividends (the dividend discount model). This means that fair value is highly sensitive to expectations about the future. The 1920s was a period of economic dynamism, where many large firms using new technologies became dominant. It is completely unsurprising that stock prices rose during the expansion.

The linkage between monetary tightening and stock prices is a standard feature of Austrian economics and/or financial market commentary, but it is not widely respected among other economic theories.