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They're both ML family languages, and both add OO, so they're not quite that closely related but they're definitely part of the same family tree.

F# at its heart is OCaml without functors, and with its original structurally typed OO model replaced by .NET's.

No, F# has a lot more OO than OCaml, and there’s a significant difference in features (ex active patterns in F#, functors OCaml). I liked what I used of F#, but for any serious program it’s more Multi-paradigm than functional, since you’ll end up doing a lot of OO.

In my experience that isn't quite true. You usually OO for IO/interop if a C# library is being used, then its module code for the most part all the way down (e.g. ASP NET Core define a class for the controller, then have it interop to F# FP code for the most parts). With some newer F# frameworks you don't even have to do that these days.

Having some experience with large scale F# codebases its rare you define a class compared to records, unions and functions. 100's of functions, 50-100 small types, 1-2 classes approx is usually the ratio I've seen for a typical microservice (YMMV).