This earlier thread in 2021 only mentions the overhead when a panic occurs, not any overhead, or lack of overhead, for simply enabling it. So this is not a complete answer.
The environment variable doesn't change what's stored, that's a compile time matter. debug and strip are the relevant compile-time options. How much difference does it make, I'm not sure of. Note also that backtraces are usually possible (or possible to attempt anyway) even with no extra information stored, as it's an operating system operation to inspect the call stack.
The variable effects panics whether and explicit backtraces attempt to capture backtraces. If you don't have either of those (or if your panics all result in termination or other scenarios where you don't care about performance), it's not going to make a difference.
One thing not mentioned above, is that if you use crates like anyhow or eyre, the same environment variable will by default also be used to determine if stack traces should be captured for normal Errors as well. That might well have a larger impact, as they tend to be more common than panics.
If I remember correctly, you can then use a separate environment variable to disable capturing backtraces on errors for those libraries, but please refer to the documentation in those cases.