`wasmtime::CoreDump::_serialize` shouldn't need a generic `T` in its store

Follow up to https://github.com/bytecodealliance/wasmtime/pull/7078#discussion_r1336021323

It is there because the method calls public APIs that require a store with a `T` but none of them actually use the `T`. For every `pub fn foo` that is called, we could create a `pub(crate) fn _foo` without the `T` and then call those methods from `_serialize` and ultimately remove the `T` from `_serialize`.

This would make it so that calling `wasmtime::CoreDump::serialize` isn't monomorphized for every `T` in a store passed to it, which can help compile times when there is more than one `T` used in the program.