I might be biased from having worked with production F#, but it feels more like functional is making its way into C#, as the general industry sees value in functional principles. So F# feels like its more here to stay?
We have access to millions of libraries. I look at BEAM languages and OCaml every once in a while but can’t quite drag myself over there, knowing that in .NET, just as an example, I can choose between a dozen JSON serialisation libraries that have been optimised and tuned comprehensively for decades.
But then, those libraries are also our curse. If you consume them, everything is OO so you either give up on functional purity and start writing imperative F# code, or you have to spend time writing and maintaining a F# idiomatic wrapper around it.
Similarly I was working recently on project to develop a library which was going to have downstream consumers. The problem lent itself really well to domain modelling in F#. But I knew that my downstream users would be C# devs. I could invest the time and write my library as “functional core, imperative shell”. But then I decided that since the interface would be OO anyway, I might as well just write it in C#.
Thankfully what keeps F# going is the wonderful community around it, not Microsoft. I know some people (outside of Microsoft) have worked on a standalone F# compiler but it’s still very early stages. Maybe one day.
C#s adoption of language features shows their utility but they’re not a replacement, per se. Without a clear functional answer in certain language and parallel computing scenarios MS would be ignored. Scala and Kotlin are comparable answers to comparable pressures on the JVM, and even keeping pace there with new and exciting tools/libraries requires some proper functional representation on the .Net platform.
F# will disappear when/if those other languages do, and already has lots of what C# is chasing with a more elegant syntax. It inherits VM and project improvements from C#, so the biggest threat to long term investment is something like the crippling changes made to FSharp Interactive (FSI), during the .Net Core transition. Otherwise it seems to be in a safe place for the foreseeable future.
C# still doesn't see itself as a functional programming language, even as it has added so many features. It may never get first-class currying or the broader ideas like generalized computation expressions, for instance. It certainly won't get F#'s cleaner syntax with fewer mandatory semicolons and whitespace nesting rather than curly brackets.
F# probably isn't going to disappear for a lot of similar reasons that GHC (the Glasgow Haskell Compiler) didn't disappear when F# was started (nor when key contributors left Microsoft). F# often already sees more outside open source contributors than contributions from Microsoft employees.