Yes, it's powered by USB while troubleshooting.
Check the voltage between GND and 5V during operation. What value do you get? USB is often not very stable in voltage if a bit of current is drawn.
I'm not entirely sure how am I supposed to add those resistors in parallel to ones on board since I most likely won't be able to solder them properly. Should I search for documentation on anything related to disabling built-in pull-up resistors or something like that is not doable? Could just use shorter cables for test purposes and see if IMU is operative with those as well.
You don't have to solder the resistors onto the board. Just connect them from SDA/SCL to 3V3.
Connecting cables are currently 1m long each, but if it somehow starts working I will most likely need to have each of them at least 2m long. This could cause an issue I suppose?
An I2C bus shouldn't be more than about half a meter in total length otherwise the signals are flattened too much from the cable capacity. Move the Arduino directly beside the IMU or use I2C bus extender chips (on both sides).