I still don’t see it as a tax, as it would be charged only if one does not provide proof of citizenship. It’s a fee charged for processing lookup of citizenship. Nothing new, additional charges levied for services rendered. If one arrives with requested documents for registering, then there is no fee, so no poll tax.
Courts have explicitly decided that all fees (refundable or not) or skills tests (even non-political basic reading comprehension) are specifically a form of poll tax and are therefore unconstitutional.
You may not see it as a tax, but courts already say it is. This was last floated in IIRC the 1960s.
Would also point out that even non-political and voluntary cost recovery, such as poor counties soliciting donations at the polls to help cover the cost of ballots has been barred as an unconstitutional poll tax.
Again, your idea is not new and has already been shot down.