GC doesn’t affect performance (at least visibly), memory allocations on critical paths do. Moreover, Rust ARC may cause memory fragmentation and perform worse than a GC.
Writing Rust, Zig, or Go, you would still control memory manually, where it matters.
It does have an impact. Discord blogged about unavoidable GC delays in go that occurred because go needed to traverse live memory, their only option (in go) for reducing that pause was to reduce the size of their data set.
GC absolutely has performance costs, even with minimal allocations, because tracing collectors must scan live objects. This is exactly what this post says. Don't know if its really improved over time in real world cases.
Writing Rust, Zig, or Go, you would still control memory manually, where it matters.