Braingolf, 6 bytes

iul1-n

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Unfortunately, Braingolf's implicit input from commandline args can't accept an all-digits input as a string, it will always cast it to a number, so instead the solution is to pass it via STDIN, which adds 1 byte for reading STDIN (i)

##Explanation:

iul1-n
i       Read from STDIN as string, push each codepoint to stack
 u      Remove duplicates from stack
  l     Push length of stack
   1-   Subtract 1
     n  Boolean negate, replace each item on stack with 1 if it is a python falsey value
        replace each item on stack with 0 if it is a python truthy value
        Implicit output of last item on stack

After u, the length of the stack equals the number of unique characters in the input, subtracting 1 means it will be 0 if and only if there is exactly 1 unique character in the input, 0 is the only falsey number in Python, so n will replace 0 with 1, and everything else with 0.

Braingolf, 6 bytes

iul1-n

Try it online!

Unfortunately, Braingolf's implicit input from commandline args can't accept an all-digits input as a string, it will always cast it to a number, so instead the solution is to pass it via STDIN, which adds 1 byte for reading STDIN (i)

Explanation:

iul1-n
i       Read from STDIN as string, push each codepoint to stack
 u      Remove duplicates from stack
  l     Push length of stack
   1-   Subtract 1
     n  Boolean negate, replace each item on stack with 1 if it is a python falsey value
        replace each item on stack with 0 if it is a python truthy value
        Implicit output of last item on stack

After u, the length of the stack equals the number of unique characters in the input, subtracting 1 means it will be 0 if and only if there is exactly 1 unique character in the input, 0 is the only falsey number in Python, so n will replace 0 with 1, and everything else with 0.