TXS0104E: Can TXS0104E support I2C and I3C protocol?

The datasheet does not mention I²C/I³C only because this devices does not have two channels.

The TXS can support all open-drain protocols. (I³C also uses push/pull signals, but the TXS should be fast enough for that.)

But TXS does not work well with large buses, where the total bus capacitance is so high that the edge accelerators time out before the voltage has reached V_CC. In that case, the remaining rising edge becomes much slower because the line is pulled up only by the two 10 kΩ resistors. (See section 4 of A Guide to Voltage Translation With TXS-Type Translators, Effects of External Pullup and Pulldown Resistors on TXS and TXB Devices, and section 3.4. of Leveraging Edge Rate Accelerators with Auto-Sensing Level Shifters.) For high-capacitance buses, (i.e., long traces, cables, or connectors), it might be a better idea to use not a passive switch like the TXS, but an I²C buffer like the TCA9803.