For figured bass, the ⁶_# figure is correct. Figured bass doesn't concern itself with chord roots, just intervals above the lowest pitch.

In functional terms, the harmony is V, with the ⁶ being a non-chord-tone anticipation of the third in the chord of resolution. It would still be noted as V⁶_#.

As a side note, cadential ⁶₄ chord are often labeled C⁶₄ to avoid the ambiguity of calling them I⁶₄ or V⁶₄.

For figured bass, the ⁶_# figure is correct. Figured bass doesn't concern itself with chord roots, just intervals above the lowest pitch.

In functional terms, the harmony is V, with the ⁶ being a non-chord-tone anticipation of the third in the chord of resolution. It would still be noted as V⁶_#. To help differentiate it from a first-inversion V chord, connecting lines could be added to show how the tones correspond to the following chord.

6 ——— 3
#

As a side note, cadential ⁶₄ chord are often labeled C⁶₄ to avoid the ambiguity of calling them I⁶₄ or V⁶₄.