When someone refers to 100A service that means per leg, right? Or is it
summed?
Per leg.
.. . .

The panel is rated 125A so that sounds like it ought to be good for 100A
service but does that mean each connector block is only good for 50A?

If the panel is rated at 125A, then the bus-bars ought to also be
rated at 125A.

Can one just have the utility give us a new drop, replace the 2 ft of wire
from meter socket to panel and the internal jumper (assuming it's not
already correctly sized, pop in a 2-100A breaker and that's that? Or is a
whole new panel a necessity? I don't want to make a small job into a major
one unnecessarily. (Moot for now as the house is not for sale but good to
know and maybe take care of in advance.)


You may not even need a new drop and service feeder, depending on
what size they are. An electrician could look at it and tell you
which bits need to be replaced, it MIGHT be as simple as just
swapping the main breaker out for a bigger one.

OTOH, replacing everything from the service drop through the
individual breakers isn't really all *THAT* major, in the grand
scheme of things. I had my service panel replaced because
it was rusting out, and upgraded my service to 200A at the
same time, all for about $1200. Since you are clearly in
a municipality where the socialists are in control, you can
probably expect to pay about double that.