So, got it running after reading up a little bit about all this I2C stuff:
Problem
The Wio LTE board delivers like I mentioned before 3.3V on the I2C bus, but the I2C_LED display needs at least something about 4.5V to 5V to function.
Solution
I cut the red and black wires on the Grove cable, connected the red wire which leads to the display to the positive connector on an external power source with 4.5V.
Important: make sure that it is the red wire which is connected to the display and not the one which is connected to the Wio LTE board. Otherwise this may kill the board.
Then I connected the black wire which comes from the Wio LTE board, the black wire which leads to the display to the negative of the external power source.
That’s it - the sketch posted above runs perfectly fine and the display shows “Hello World!”.