I have no experience converting a C or C++ project to Rust but have transitioned Objective-C projects to Swift and have found that even with Obj-C's newer additions to improve Swift interop, making the project as a whole safe is difficult until you've factored Obj-C out of all critical paths. It's just too easy for things to go wrong in the Obj-C half or in the Obj-C → Swift interop.

So almost unavoidably you end up with two refactors: first, the piecemeal rewrite in the the safer language, and then a second when the original language has been rooted out and you can take advantage of all of the features of the new language.