This is a 200 amp meter base, I've never upgraded an undergound service. Which is why I'm asking, not sure if the POCO underground needs to be changed it looks plenty big enough. I would change the conductors between the base and the panel of course.
I've always left the 200A meter pan in place. If it's in really bad condition then it's a different story. Otherwise there's really no reason to change it.
I missed the fact that it is underground. Generally underground services, at least around here, terminate in a 200 amp base. I bet you are probably not adding that much load but you definitely need to contact the poco. Many of them will have run 200 amp wire for a 200 amp base.
I always call poco since an inspection is needed anyway.