GDScript will likely be supported for a long time (as long as Godot is relevant). I doubt they would drop it, for the same reasons they used a custom language to begin with.
C# is open source under decent licenses (MIT, Apache), and I doubt Microsoft will try to do anything dumb with the licensing. Even if they did, current versions could still be used.
And they recently added the real .NET to Ubuntu (not the community Mono project) and this version is what Godot 4.0 uses, so if anything they are more open to Linux and open-source, not less.
Personally, I think C# is more suited to application development, I never thought it worked well as a scripting language. But it is better than Java, for sure, and similar enough to C/C++ that it's not hard to learn.
But I like to work quickly. GDScript, or Python-like languages, are much better for that. LUA is also good. I just don't feel like "real" programming languages are a good fit for gameplay scripting.