The std::time::Instant type used in the egui-winit crate is not supported when running through WebAssembly:
panicked at 'time not implemented on this platform', library/std/src/sys/wasm/../unsupported/time.rs:13:9
WebAssembly could potentially be supported in egui-winit by using a crate such as https://github.com/sebcrozet/instant instead, which only re-exports the std::time::Instant type on native but implements a polyfill for WebAssembly targets.