How do I make my bathroom pipes more practical?
The relatively fixed elements are the drain  pipe going trough the floor and the vent pipe running to the left. It is complex to change where these exit the room (go into the wall or floor).

As other comments and answers suggest, you can probably shift these pipes toward the back of the vanity.  With the vanity removed, you can put in a "sweep elbow" (a shallow curve rather than a sharp 90 degree) from the pipe coming up through the floor toward the back of the cabinet area.  You can then turn it upward, again with a sweep elbow, and join the P-trap to that upright pipe.

If the sweep elbow is higher than the floor of the vanity, you can open up the floor to lower it or you can take out a channel in the vanity floor to accomodate.  This should still leave enough room higher up to accomodate drawers on one side ot the other.

The vent stack can also be turned toward the back to meet the newly routed drain stack.  Elbows in vents are less critical than waste elbows.