Anyway, the typical implementation involves two phases, one which uses a table to identify the matxhing catch clause, then another one going through landing pads for each frame of the stack. Just consult the Itanium ABI spec for technical details.
Here's a simple example showing exceptions vs. sum types: https://godbolt.org/z/9Er6eKxs9
In the non-throwing exception path, there's literally no error or exception handling code executed at all. Whereas in the sum-type error-returning version, you have a branch at every call site that's always executed regardless of if there's an error or not.
Now the exception handler generates ".cold" clones of the function, so the total assembly for the exception handling one is larger. However, that assembly isn't every executed if an exception isn't thrown, which is the broader point. So it's not taking up CPU cache space & it's not taking up branch predictor slots.