Multiple pull up for I2C pins
It is typically acceptable to add an external resistor in all cases. Including when there is a small voltage mismatch. If you calculate the current from your example above, the MCU pull-up (assuming. 22k internal) would be dissipating \$ (1.90-1.83)^2/22k = 220nW\$.


With I2C the only real concern is that you have a range of pull-up resistance to handle the following two requirements:



You provide enough current to quickly pull the line high (give
it a good edge).
You have enough resistance to prevent the
devices internal transistors from overheating or not having enough
conduction to pull the line low.


Keep in mind the total line resistance to Vcc will be the parallel combination of all pull-ups, internal and external.

Finally to address your question about effecting the power rail, assuming you have good power regulation, the difference in voltage should be dissipated across the resistance. If you have a high impedance source, you could see a small effect to the supply bus. Really this is application dependent.