I get the feeling F# is a second-class citizen in the ecosystem. How likely is it (or is it at all possible) that I'm going to run into some library that doesn't work with F#?
You're right that it's a second-class citizen.
This isn't true, C# has been adding new ABI features that didn't interact correctly with F# until the compiler and tooling catched up. For example, the spanification of C# was a huge a pain point and it still is when it comes to tooling.
Since its introduction that CLR has the notion of CLS, the Common Language Subset, that any language targeting the CLR should be able to understand.
Anything in the MSIL or metadata, that isn't part of that, requires additional effort from the respective language to be able to expose those features, and many of the more recent improvements, are more in the sense of CLR meaning C# Language Runtime, than Common Language Runtime.
For example, F# used to crash the CLR with InvalidProgramException when setting C# `init` properties. [1] It took almost three years, I think, to release the fix.
[1]: https://github.com/fsharp/fslang-suggestions/issues/904
Another rough example would be spans, and their more general feature, byref-like types (ref struct). These required plenty of compiler support, as they've got special lifetime rules (and more pending to implement `scoped`), they are banned as generic type arguments, and they require ignoring a special Obsolete attribute.
While these were added to F# timely, many language features still break when they interact with them: local functions, computation expressions (even the built-in ones), recursive type inference, and generic intrinsic methods such as `raise`, `defaultof` or `typeof`.
This wouldn't be so bad if C# hadn't "spanified" the shared framework and the entire ecosystem without CLS alternatives for many APIs.
So, these natural F# snippets don't compile:
let numbers = [| for span in text.EnumerateLines() -> Int32.Parse span |]
let checkNonEmpty (span: ReadOnlySpan<'T>) =
if span.Length > 0 then span else failwith "Expected non-empty span."
Generally though, it's pretty easy. Sometimes you'll want to make bindings around various things (not that you need to, but it'll make things smoother).
It's not actually awful, it's just that there's no real documentation of "hey today we're going to take Serilog/whatever and show you how to configure it in F#" style videos, so depending on where your weaknesses lie it can feel frustrating.