So, here are my 2 cents for your problem: I would recommend slow code conversion or, rather, refactoring for Swift, if required for new parts of the code. In addition, if the converted code is currently used in other side projects (function branches, etc.), you cannot guarantee that it will work anyway.
I hope you got unit tests in place because they could make life easier. In any case, consider the aspect of regression testing your application functions. The libraries you use should now be frameworks (some libraries may not compile as Framework, keep this in mind).
IF you really want to convert the code base, I would do it chirally.
Consider the entire Application Layer and within this layer specific classes.
Start writing tests for these classes (you can do it in Swift too), Unit Test, integration test, user interface tests
Convert a class to a fast class (remember that some logic may change, and other functions will also be affected)
Implement a bridge header (if necessary) that you can use as the Application Layer interface for other interfaces - this will even improve your understanding of how different parts of the code play together. If you notice any strange statements. Publicity, too many random accesses for different classes or something else. Do not touch it. Actually note that down
Do extensive tests of your little change
Start over with the next class.
If all classes have finished at your current application level and you haven’t broken anything. Great job. Now take a look at your notes.
Continue from the next layer.
In short: I would only convert these parts to Swift, which in any case must be changed (refactoring, new functions, errors, whatever). If the code worked, and you see no other reason than “okay, now it's Swift”, I would take into account only the conversion, if I really had time for this, otherwise you could break the working code or even which was installed , which in some cases is different for Swift and Objective-C.
If you really feel that you are the person for this: I would start writing tests ;-) Unit-, Integration and UI Tests. This will help you with your CURRENT code base, but also with your future code base, whether in Objective-C or Swift. And this is a great help for converting code to Swift.
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