The recursive backtracking structure is clear, what did you to reach sub 3s performance?

Hi Kacarott, I have corrected myself in the 2nd reply; sorry about the confusion.

As mentioned in the 2nd comment in the question, "the minimum requirement for unique solution is 17 givens" is a bit misleading.
17 is not a condition to have multiple solutions.

Also note that over 500 people have solved this in Python, so the chance that all 500 of them made the same error as the checker in order to pass is very unlikely. I am going to close this, but you can post more evidence if you are convinced there is a problem.

The two solutions you showed in the original post are not the same, they are different. Have a look at both of them where I've marked Xs.

[9, 3, 8, 5, 1, 7, 2, 6, 4]
[2, 5, 7, 8, 4, 6, 3, 1, 9]
[6, 1, 4, 2, 9, 3, 8, 7, 5]
[5, 4, 9, 3, 2, 1, 7, 8, 6]
[7, 8, 2, 6, 5, X, X, 3, 1]
[1, 6, 3, 7, 8, X, X, 5, 2]
[4, 2, 5, 1, 3, 8, 6, 9, 7]
[8, 7, 1, 9, 6, 2, 5, 4, 3]
[3, 9, 6, 4, 7, 5, 1, 2, 8]

Therefore there is no unique solution.

I took another look, the solver is correct; the assumption that givens >= 17 would guarantee a unique solution is falsy.

Puzzle:
[8, 0, 0, 0, 0, 5, 0, 0, 0]
[0, 0, 0, 8, 0, 4, 0, 0, 0]
[0, 0, 0, 3, 0, 0, 0, 0, 6]
[0, 8, 0, 0, 0, 9, 7, 4, 3]
[0, 5, 0, 0, 0, 8, 0, 1, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 7, 0]
[0, 3, 0, 5, 0, 0, 0, 8, 0]
[9, 7, 2, 4, 0, 0, 0, 5, 0]

Solutions:
[8, 9, 1, 2, 6, 5, 4, 3, 7]
[6, 2, 3, 8, 7, 4, 1, 9, 5]
[7, 4, 5, 3, 9, 1, 8, 2, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[4, 5, 7, 6, 3, 8, 9, 1, 2]
[3, 1, 9, 7, 4, 2, 5, 6, 8]
[5, 6, 8, 9, 1, 3, 2, 7, 4]
[1, 3, 4, 5, 2, 7, 6, 8, 9]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 9, 1, 2, 6, 5, 4, 3, 7]
[6, 2, 3, 8, 7, 4, 1, 9, 5]
[7, 4, 5, 3, 9, 1, 8, 2, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 7, 6, 4, 8, 9, 1, 2]
[4, 1, 9, 7, 3, 2, 5, 6, 8]
[5, 6, 8, 9, 1, 3, 2, 7, 4]
[1, 3, 4, 5, 2, 7, 6, 8, 9]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', '-', '-', 'X', '-', '-', '-', '-']
['X', '-', '-', '-', 'X', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 2, 3, 6, 1, 5, 4, 9, 7]
[6, 9, 7, 8, 2, 4, 1, 3, 5]
[1, 4, 5, 3, 9, 7, 8, 2, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 4, 7, 6, 8, 9, 1, 2]
[7, 1, 9, 2, 4, 3, 5, 6, 8]
[5, 6, 8, 9, 3, 1, 2, 7, 4]
[4, 3, 1, 5, 7, 2, 6, 8, 9]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', 'X', 'X', 'X', 'X', '-', '-', 'X', '-']
['-', 'X', 'X', '-', 'X', '-', '-', 'X', '-']
['X', '-', '-', '-', '-', 'X', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', 'X', 'X', 'X', '-', '-', '-', '-']
['X', '-', '-', 'X', '-', 'X', '-', '-', '-']
['-', '-', '-', '-', 'X', 'X', '-', '-', '-']
['X', '-', 'X', '-', 'X', 'X', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 2, 1, 9, 6, 5, 4, 3, 7]
[6, 9, 3, 8, 7, 4, 1, 2, 5]
[7, 4, 5, 3, 2, 1, 8, 9, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[4, 5, 7, 6, 3, 8, 2, 1, 9]
[3, 1, 9, 7, 4, 2, 5, 6, 8]
[5, 6, 8, 2, 1, 3, 9, 7, 4]
[1, 3, 4, 5, 9, 7, 6, 8, 2]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', 'X', '-', 'X', '-', '-', '-', '-', '-']
['-', 'X', '-', '-', '-', '-', '-', 'X', '-']
['-', '-', '-', '-', 'X', '-', '-', 'X', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', 'X', '-', 'X']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['-', '-', '-', 'X', '-', '-', 'X', '-', '-']
['-', '-', '-', '-', 'X', '-', '-', '-', 'X']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 2, 1, 9, 6, 5, 4, 3, 7]
[6, 9, 3, 8, 7, 4, 1, 2, 5]
[7, 4, 5, 3, 2, 1, 8, 9, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 7, 6, 4, 8, 2, 1, 9]
[4, 1, 9, 7, 3, 2, 5, 6, 8]
[5, 6, 8, 2, 1, 3, 9, 7, 4]
[1, 3, 4, 5, 9, 7, 6, 8, 2]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', 'X', '-', 'X', '-', '-', '-', '-', '-']
['-', 'X', '-', '-', '-', '-', '-', 'X', '-']
['-', '-', '-', '-', 'X', '-', '-', 'X', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', '-', '-', 'X', '-', 'X', '-', 'X']
['X', '-', '-', '-', 'X', '-', '-', '-', '-']
['-', '-', '-', 'X', '-', '-', 'X', '-', '-']
['-', '-', '-', '-', 'X', '-', '-', '-', 'X']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 2, 1, 9, 6, 5, 4, 3, 7]
[6, 9, 3, 8, 7, 4, 1, 2, 5]
[7, 4, 5, 3, 1, 2, 8, 9, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 7, 6, 4, 8, 2, 1, 9]
[4, 1, 9, 7, 2, 3, 5, 6, 8]
[5, 6, 8, 2, 3, 1, 9, 7, 4]
[1, 3, 4, 5, 9, 7, 6, 8, 2]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', 'X', '-', 'X', '-', '-', '-', '-', '-']
['-', 'X', '-', '-', '-', '-', '-', 'X', '-']
['-', '-', '-', '-', 'X', 'X', '-', 'X', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', '-', '-', 'X', '-', 'X', '-', 'X']
['X', '-', '-', '-', 'X', 'X', '-', '-', '-']
['-', '-', '-', 'X', 'X', 'X', 'X', '-', '-']
['-', '-', '-', '-', 'X', '-', '-', '-', 'X']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 9, 3, 6, 1, 5, 4, 2, 7]
[6, 2, 7, 8, 9, 4, 1, 3, 5]
[1, 4, 5, 3, 7, 2, 8, 9, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 4, 7, 6, 8, 9, 1, 2]
[7, 1, 9, 2, 4, 3, 5, 6, 8]
[5, 6, 8, 9, 3, 1, 2, 7, 4]
[4, 3, 1, 5, 2, 7, 6, 8, 9]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', '-', 'X', 'X', 'X', '-', '-', 'X', '-']
['-', '-', 'X', '-', 'X', '-', '-', 'X', '-']
['X', '-', '-', '-', 'X', 'X', '-', 'X', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', 'X', 'X', 'X', '-', '-', '-', '-']
['X', '-', '-', 'X', '-', 'X', '-', '-', '-']
['-', '-', '-', '-', 'X', 'X', '-', '-', '-']
['X', '-', 'X', '-', '-', '-', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

[8, 9, 3, 6, 1, 5, 4, 2, 7]
[6, 2, 7, 8, 9, 4, 1, 3, 5]
[1, 4, 5, 3, 2, 7, 8, 9, 6]
[2, 8, 6, 1, 5, 9, 7, 4, 3]
[3, 5, 4, 7, 6, 8, 9, 1, 2]
[7, 1, 9, 2, 4, 3, 5, 6, 8]
[5, 6, 8, 9, 3, 1, 2, 7, 4]
[4, 3, 1, 5, 7, 2, 6, 8, 9]
[9, 7, 2, 4, 8, 6, 3, 5, 1]

['-', '-', 'X', 'X', 'X', '-', '-', 'X', '-']
['-', '-', 'X', '-', 'X', '-', '-', 'X', '-']
['X', '-', '-', '-', 'X', 'X', '-', 'X', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']
['X', '-', 'X', 'X', 'X', '-', '-', '-', '-']
['X', '-', '-', 'X', '-', 'X', '-', '-', '-']
['-', '-', '-', '-', 'X', 'X', '-', '-', '-']
['X', '-', 'X', '-', 'X', 'X', '-', '-', '-']
['-', '-', '-', '-', '-', '-', '-', '-', '-']

Potential an error in the checker script:

The following input generates a false error message "invalid should raise error":
I have (possibly) replicated how to the two solutions are found on different paths, but they are the same.
Below is my results without early exit; with givens == 27, the question cannot have multiple solutions.

givens =  29
Puzzle:
[9, 0, 0, 5, 0, 0, 0, 0, 4]
[0, 0, 7, 0, 4, 0, 3, 0, 0]
[6, 0, 0, 0, 0, 3, 0, 7, 5]
[0, 4, 0, 0, 2, 0, 7, 0, 0]
[7, 0, 2, 0, 0, 0, 0, 0, 1]
[0, 0, 3, 0, 8, 0, 0, 5, 0]
[4, 2, 0, 1, 0, 0, 0, 0, 7]
[0, 0, 1, 0, 6, 0, 5, 0, 0]
[3, 0, 0, 0, 0, 5, 0, 0, 8]

Solutions:
[9, 3, 8, 5, 1, 7, 2, 6, 4]
[2, 5, 7, 8, 4, 6, 3, 1, 9]
[6, 1, 4, 2, 9, 3, 8, 7, 5]
[5, 4, 9, 3, 2, 1, 7, 8, 6]
[7, 8, 2, 6, 5, 4, 9, 3, 1]
[1, 6, 3, 7, 8, 9, 4, 5, 2]
[4, 2, 5, 1, 3, 8, 6, 9, 7]
[8, 7, 1, 9, 6, 2, 5, 4, 3]
[3, 9, 6, 4, 7, 5, 1, 2, 8]

[9, 3, 8, 5, 1, 7, 2, 6, 4]
[2, 5, 7, 8, 4, 6, 3, 1, 9]
[6, 1, 4, 2, 9, 3, 8, 7, 5]
[5, 4, 9, 3, 2, 1, 7, 8, 6]
[7, 8, 2, 6, 5, 9, 4, 3, 1]
[1, 6, 3, 7, 8, 4, 9, 5, 2]
[4, 2, 5, 1, 3, 8, 6, 9, 7]
[8, 7, 1, 9, 6, 2, 5, 4, 3]
[3, 9, 6, 4, 7, 5, 1, 2, 8]