I suppose language wise the support is there but there are lack of libraries. A while ago I was consider considering F# for the backend. While looking for database client I found most third party like SQLprovider, rezoom.sql didnt support .net core very well.

SQLProvider has been ported to .NET Core - I've used it no problem when scripting/prototyping across a variety of different data sources at once. Admittedly I tend to just use straight ADO.NET anyway - its simple enough to use and with F# your not saving all that much code/if at all moving to Dapper since the language tends to be more succinct.