The oscilloscope traces show that SCL and SDA signals have a time constant that's way beyond what'd be required at the frequency your run the bus at. I'm seeing approximately a 20us time constant.
The circuit as you describe it should have a capacitance between SCL/SDA and ground less than 100pF. Together with I2C's recommended pull up on the order of 10kOhm, we should be seeing a time constant of 1E-10F * 1E4Ohm = 1E-6s = 1us.
But we're seeing 20us time constant (roughly) instead. So, you're not telling us something. Either you have connected ~2nF of capacitance between each line and a low impedance node (either power supply rail for example), or you don't have the 10kOhm pull-ups in place.
If you didn't stick extra capacitors there, it looks like you have about 200kOhm-1MOhm pull-up resistance - one to two orders of magnitude too high, depending on what the parasitic capacitance is on those lines.
Such pull-up resistance would be in the range of weak pull-ups on microcontroller GPIO pins. So it looks like you're trying to run I2C with nothing but weak pull-ups in the microcontroller. That's not enough. Connect 10-15kOhm between SCL and I/O supply voltage, and similarly for SDA.