Free databases on the issues of commercial banks are located in central banks, banking supervision institutions, financial system supervision and other public institutions supporting the development of the banking sector.
For European Banks you can get databases on the ECB website. For international macro data and general information you can go to IMF. And if you have phd or lecturer account in any university I suggest asking your university manager if you have license for Statista or The Banker, both very useful. Only if it is of your interest, in my PhD I´m deep diving into Spanish banking industry, setting a propietary database with key data and information about both public/listed and non listed banks. Best regards. Enrique