It's not just Java/Kotlin that want GC in Wasm. One major implementation that's already in use is .NET's Blazor, with a less than ideal impl.:
https://dotnet.microsoft.com/en-us/apps/aspnet/web-apps/blazor
Also see:
https://github.com/WebAssembly/gc/issues/77
Access to a GC would benefit non-managed languages too, like Rust, because some objects/resources need shared ownership between WASM land and JS land, so having access to the browser's GC from Rust/WASM is valuable actually.