Minimum value I2C-pull up resistor for arduino
The full datasheet of the atmega328p can be found here: https://www.microchip.com/wwwproducts/en/ATmega328P.
It is called "ATmega328/P AVR MCU with picoPower Technology Data Sheet".

In section "32.7 Two-Wire Serial Interface Characteristics" in table 32-10 on page 372 it shows different voltage levels for the input.

On page 110 it says: "When the TWEN bit in TWCR is set (one) to enable the 2-wire Serial Interface, pin PC4 is disconnected from the port and becomes the Serial Data I/O pin for the 2-wire Serial Interface. In this mode, there is a spike filter on the pin to suppress spikes shorter than 50 ns on the input signal, and the pin is driven by an open drain driver with slew-rate limitation".

I wrote here before that the i2c (the twi hardware inside the microcontroller) did not use the digital pin hardware. However, the i2c pins can still sink a lot of current. Thanks to @Berkay for noticing the same behaviour of the sink current as a normal digital pin.

According to the datasheet the atmega328p of the Arduino uno might not use the digital pin hardware for i2c. It is not known if the same mosfet circuit is used with the same (large) sink current. Perhaps the chip uses a similar mosfet circuit with added slew rate for the output and added spike filter for the input. Perhaps the same mosfet of the digital pin is used after all.

In the Arduino sketch, calling Wire.begin turns on the dedicated i2c hardware in the atmega328p chip. The sink current and voltage levels are according to the i2c specifications.
As you can see in the i2c tutorial by Nick Gammon, the Arduino can sink more than 3 mA.

When the pullup resistors are too low, for example for a sink current of 4 mA, the Arduino uno can handle that, but the slave might not.

When all the pullup resistors are combined, the required sink current can be calculated. The maximum is 3 mA to meet the i2c specifications. To compensate for wire capacitance the i2c bus speed can be lowered.

The i2c bus is not ment to go into a cable, it is not ment for long wires. A cat6 cable is 46 pF/m. That means your 800 pF is for 17 meters cable? That is not what the i2c bus is for. It is for 17 centimeters. The rule of thumb is maximum 50 cm for a normal 100 kHz to 400 kHz i2c bus.