That's a really tough question.
I will invest time in learning rust this year, but I have already been coding in C++ the last 6 years.
The thing about C++ is that it is such a large and powerful language that it is extremely hard to decide which parts to focus on. The basic syntax isn't that hard, but learning about the standard library, performance considerations, ... is time consuming.
I have a somehwat hard time with rust though, because a lot of the restrictions that the compiler enforces are really tight, especially when you dabble with generics for numerical computing.
Nobody knows what will win in the future, but I think Rust is the future for a lot of things that are done in C++ right now. C++ will not vanish due to the huge amount of legacy code, but I am not too positive about the future development of the language. There is only few fresh blood in the development of the language and the tooling is archaic compared to many other languages. I really do like C++ but I don't see much of a future there.
Rust will become more relevant in many areas such as (larger) embedded systems, security related fields, tooling, ...
Not sure if you have a timeline for when you want to get a new job. I would learn Rust first. Maybe your current company even pays you a one week training or something like this. This will give you the basics and from there I would just go and start writing rust for small helper tools. With a background in Rust, C++ will feel really old and not fun at all, but modern C++ and Rust aren't too different regarding their memory management philosophies.