Those are cast into block/transmission and not a hole.... there is no sealing gasket in there.
That said there is whats called a rear main seal that is on the back of the engine block that is leaking and dripping down the back through those ‘holes’.
Is it serious... yes and no....its common issue as the engine gets older and rolls more miles and the transmission needs to be removed to fix it and there are specialized tools to install (although not really needed but recommend) How much oil are you losing, have you checked the dipstick? Are there drips on the floor? Etc. Once it starts it will just get worse over time/miles. Do you have to get it done tomorrow, no, you can shop around to diff mechanic/dealers to get a few quotes but I personally would stay away from the dealership. Cost will vary in different areas of the country and from dealer to private mechanic and if you have 2wd vs 4wd(awd) etc. You are going to spend a MINIMUM of $600 and that’s because it is labor intensive yet the seal is relatively cheap...hope this helps