The whole magic about CL's condition system is to keep on executing code in the context of a given condition instead of immediately unwinding the stack, and this can be done if you control code generation.
Everything else necessary, including dynamic variables, can be implemented on top of a sane enough language with dynamic memory management - see https://github.com/phoe/cafe-latte for a whole condition system implemented in Java. You could probably reimplement a lot of this in WASM, which now has a unwind-to-this-location primitive.
Scheme doesn't have restarts as a core concept like Common Lisp, but it does have continuations. For the Scheme implementation I worked on [0], the exception system is built on top of the continuation system. In other words, Scheme exceptions are not Wasm exceptions. However, we did find a use for Wasm exceptions in the implementation of the runtime. We realized it would be useful to mark the entry point into Scheme with a Wasm 'try' block for re-entrancy reasons. Programs might call from Scheme to JS back to Scheme and on and on. When we suspend the current continuation we throw a Wasm exception and find the correct entry point for doing our stack tomfoolery, re-throwing until we find it. I don't know if my explanation makes any sense but that's how we're using Wasm exceptions.
