I’ve found working with Rust and Bevy to be quite pleasant. If you’re used to working with ECS, I suggest you at least give it a go.
Rust is as functional as C++ 20 with ranges and views is, which is to say it isn’t. Not sure where you got that impression from, but while it does borrow some ideas from functional languages, it’s still very much a procedural one.
Zig doesn’t have headers, nor inheritance. Again, not sure where you got that from, but Zig is basically a modern C, so there’s no OOP anywhere, let alone multiple inheritance.
As for what to use, I think they’re both viable alternatives. I lean more towards Rust, but that’s just due to familiarity. Odin also looks like a viable option, if you don’t mind a smaller ecosystem.
If you want a garbage collected language, then I’d go for C#. Despite its historic reputation as a Windows only language, it’s been cross platform and open source for roughly a decade at this point. I find it great to work with.
The fact that it can be used as a scripting language doesn’t mean it’s a scripting language. You could use C++ as a scripting language as well, but it would suck.
C# even supports native compilation nowadays, not just JIT, so it’s definitely not a lowly scripting language.
Anyways you’ve got options. Go may also be one of them if you want GC, I forgot to mention it.