Seems like that’s TI TXS0108ERGYR
The low level output voltage graphs on P14 show a maximum current of 1000 uA giving about a 0.5 V output.
The pull-up resister on the B (3.3V/5V) port side is 4k when the output is high , 40k when low. (Section 8.2, P17, under the diagram)
So the maximum current at 5V would be 1.25 mA with the output connected directly to ground.
Which is which I got from your measurements earlier…