Indeed, it is interesting that one of them works and one does not.
Especially since the TXS0102 should work as it is even intended for that, and TXS0108 should not work as it seems to be unsuitable for I2C bus.
By looking at the scope captures, both the rising and falling edge look very slow. I would expect the falling edge to be very sharp compared to the rising edge, as the falling edge needs to be faster than 300ns. Which was fixed by changing from 1x to 10x. Now the glitches caused by rise time acceleration are clearly visible.
However, unless you specifically need edge time accelerators on your bus, I would not use either of these two chips just for simple voltage translation.
So the TXS0102 should work, but it depends on your external circuitry if it works or not. The TXS0108 should not even work, but again, it depends on your external circuitry. What matters are the bus capacitances, bus voltages, external pull-ups, chip drive strength, and even bus length.
You need to look the bus with an oscilloscope to see why it fails to work.
Both translator chips seem to require or cause faster transitions on bus than typically found on I2C bus. These level converter chips contain active circuitry in them, to accelerate logic signal edges. In fact the accelerated edge time may be less than what is allowed on an I2C bus.
However, what explains the difference in their operation is their internal structure. The 0108 has both rise and fall time accelerator, while the 0102 only has a rise time accelerator. When a transition edge is detected, the chips will momentarily drive the bus hard to the same state to make the transition faster, but this is not allowed by I2C, and it can cause problems, unless the chip does it in a way that is specifically compatible with I2C.
The 0108 has 40kohm pull-ups when idle, and 4k during rise time acceleration, and accelerates both rising and falling edges.
The 0102 has only 10k pull-ups and accelerates only rising edge.
So there is enough of internal differences between the chips.