> I find that the most common reason I go back to check a variable declaration is to determine the type of the variable,

Hover the mouse cursor over it. Any reasonable editor will show the type.

> In Rust, in particular, this leads to some awkward syntactic verbosity, because mutable variables are declared with `let mut`, meaning that `let` is used in every declaration.

Rust is very verbose for strange implementation reasons... namely to avoid parse ambiguities.

> In C or C++ the type would take the place of that unnecessary `let`.

OTOH, that means you can't reliably grep for declarations of a variable/function called "foo". Also consider why some people like using

    auto foo(int blah) -> bool

style. This was introduced because of template nonsense (how to declare a return type before the type parameters were known), but it makes a lot of sense and makes code more greppable. Generic type parameters make putting the return type at the front very weird -- reading order wise.

Anyhoo...