I2C Overshoot with Teensy 4.1 and TCA9406 Level Shifter
The level translator chip might be more complex than what you would expect from a simple I2C level translator. It has internal push stage for rise time acceleration and can work up to 2 Mbps opendrain signals and 24 Mbps pushpull signals. So if you have no load connected, also the rising edge is accelerated to look like square wave when there is no load. The chip also has internal 10k pull-ups to respective supply which is very light load.
So with incorrect probing techniques and incorrectly compensated probes, the insides of the level translator chip explains the overshooting and undershooting that you see on the scope. You did use the ground spring, also make sure the probes are at 10x setting, and that the probe compensation is properly adjusted.
I also recommend to switch to more normal level translator chip than TCA9406.
Definitely put separate I2C pull-up resistors, as you can just leave them out if you don't need them.