I am wondering to which extent versions of the DDM formula(https://en.wikipedia.org/wiki/Dividend_discount_model) is used by large banks and institutional investors etc, in some sense anyone who is not a retail investor.
DDM definitely used in practice. Probably the Two Stage Dividend Discount model is used more often that the 1 stage or Gordon model described in the Wikipedia article.
From time to time there are surveys of techniques used by equity analysts, for example Equity Valuation: A Survey of Professional Practice by G. Pinto (2005), SSRN 2657717. You can see some figures concerning DDM on Page 5 and on Page 17, or read the entire report for more details. It may not be the most popular technique but is used in a substantial number of cases.