Clogged clawfoot bathtub drain

We have a slow bathroom drain (I squarely blame the sissy bodywashes and scrubs), and now the bathroom sink water has also started to flow into the tub instead of down the drain.
I have emptied a few gallons of liquid plummer, etc. into the bathtub drain and also tried using an auger/ snake, but didn’t get very far into the drain (I went in through the tub overflow drain opening).
Any tips?

By ohiise |