Difficult to say, as that information is not gathered by Atlassian (they may well ask, but it's voluntary and ignored).
You could ask them about stats for "database usage you see in your support calls", as they do ask when you raise a call, and there's no reason for someone asking for help to lie. But I suspect that would not really be representative, because some databases are better (for JIRA) than others, so the flakier ones would result in more support calls, and hence skew the figures.
In my experience though, MySQL is top of the list, with PostGreSQL in a close second place. Oracle is a distant third, with MS-SQL close behind it. But I've been deliberately vague there because most of my experience is in large corporate environments. There could be a very different pattern in smaller users, not-for-profit places, single-product development organisations, government bodies etc etc etc.
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