An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed.[1] This definition excludes the related palindromic primes.
Source: https://en.wikipedia.org/wiki/Emirp

By that definition you should expect to find some functions that express the main idea of a backward prime and by that I mean a way to know if a number is a palindrome, to reverse a number and if it's prime and therefore backward_prime should somehow call them.
It's a good practice to express in your code a language that show the main ideas of the people that bring you the problem.
I advice you to read a little about TDD.

Good solution but can get hard to read.

is_not_palindrome
Is not a good practice to use negatives in your signatures. is_palindrome could be better.

Execution Timed Out (12000 ms) in Rust and it surely did not run for 12000ms.

explain further since you aren't making any sense.

It was written before ..= was stabilized.