In C++, “overloading” is a mechanism for providing a custom definition for existing operators so they can be used in custom types, not a mechanism for adding new operators to the language. You can’t change the meaning of a “=>” operator because C++ (as of this writing at least) doesn’t have a “=>” operator.
As a supplement to Jerry’s great answer, I want to point out that this was not an oversight by any stretch, but a very conscious design decision. Bjarne Stroustrup, the original creator of the C++ language, describes his thoughts on this in his fabulous book “The Design and Evolution of C++”, as I quote here:
I [Stroustrup] considered it important to provide overloading as a mechanism for extending the language and not for mutating it; that is, it is possible to define operators to work on user-defined types (classes), but not to change the meaning of operators on built-in types. In addition, I didn’t want to allow programmers to introduce new operators. I feared cryptic notation and having to adopt complicated parsing strategies like those needed for Algol68.”
(bold emphasis mine, italics in the original)
Source: Stroustrup, Bjarne: “The Design and Evolution of C++”, Addison-Wesley, 1994. §3.6.5
PS: Although a bit dated as a reference for modern C++ design, this is an excellent and fascinating source to explore the history and the reasoning that led to the design of the original C++ language. The language further design has long been under the purview of an ISO Standards committee but its continuous evolution has continued to be driven by many of the same principles described in the book and Dr. Stroustrup continues to be an important voice in that evolution process.