&str is a "string slice", that's true. This means that it's more specific than other kinds of slices, and so does not support every operation that slices do.
The key question that needs to be answered is: iterate over windows of what? Bytes? Codepoints? Grapheme clusters?
May I suggest the unicode_segmentation crate?
It will do what you want for ASCII, with the added benefit that if you ever extend to non-ASCII it'll just keep working.