The SALT (state and local taxes) is limited to $10,000 ($5,000 if Married filing separately).
Are you sure that after entering all your itemized deductions including property tax, yor itemized deductions are greater than than your standard deduction?
Your observations lead me to think that your total itemized deductions (including property tax) are lower than your standard deduction. This is why adding or leaving out property tax has no effect on your tax due.
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