Spaces vs Circuits
First let's explain the 8/16 thing, or "8 spaces but 16 circuits". At some point, panel manufacturers developed what I (alone) call a "double-stuff" breaker, which crams 2 breakers into a single space. This is intended to solve crowding problems in too-small panels.
photo source: Home Depot
Relying on these, marketing called their boxes 2X-circuit (X-space). Around 2014 they mysteriously stopped doing that. Recent NEC changes required AFCI or GFCI breakers on damn near every circuit... AFCI and GFCI are not made in double-stuff breakers.
Your 16/8 service panel is a legacy of that bad labeling. You have an 8-space panel, intended to replace an 8-space fuse box.
Panel space is dirt cheap. Go nuts.
You are dreaming of a 16-space panel. And even that is dreadfully small and you will find it rather limiting even with 100A service.
The practice of many electricians is to give you the smallest panel possible. That's first, to force you into more subpanel work if you expand further (more money for them) and second to save themselves $20 in part cost.
The cost of a larger panel is trivial tiny compared to total project cost. It is very correct to be extreme. Please spend an extra $100 for a 42-space panel, unless you just can't make it fit. Honestly I'd go 60-space. Not least, those larger panels are 225A-ready.
You never know. You might do a kitchen remodel and go hey, I'd like a separate circuit for refrigerator done microwave done dishwasher done disposal done 3 outlet circuits done. You have the space.
When you buy a PC, do you really calculate your needed hard drive space and buy just what you need... Or do you just buy the big 3TB drive? Of course you do. Same thing here.
More work to do at the meter
OK so the power company says their side of the cable is 320A. If they say so.
They say their meter is 320A. If they say so.
But your meter housing is not 320A.
To support more than the listed 125A, you will need to upgrade your meter housing. There's no question of that. That's your equipment and you have to pay for it, probably, unless your power company does something different with cost sharing.
You won't be able to replace parts of it, you will probably even have to replace both sides of it as a single unit. However it is very nice to have your main breaker in the meter. It means you can fully de-energize your main panel, which makes it safer for you to do yourself.
The 320A may be shared
Since it's multi-unit, the power company provisioning 320A makes more sense. Trouble is, this 320A service is probably shared between both units. So it's not as much as you think.
You really need to talk to your power company about what they consider this "320A" to be. It may be a relabeling of what other power companies call 400A service. So they may be willing to feed two 200A panels, or 100/100/200. This is a conversation you can have only with them.
More food for thought is sub-metering units, and separately metering common spaces. The new thing in rental properties is to have one main meter and the landlord has sub-meters per tenant. Many landlords prefer (and some law requires) commons space usage to be on a separate (sub) meter, i.e. heating, yard and commons lighting, anti-freeze pipe wrap or roof/gutter heat, coin laundry, Christmas decorations etc.
No, you can't
Since your panel isn't listed and labeled to have a breaker put there (the wiring diagram on the panel label would show a set of usable spaces there if they were intended to be used), it can't have a breaker put there (not without violating NEC 110.3, that is). You'll have to find a different way to fix the space problem (perhaps with the aid of double-stuff breakers?)
While you're in there...
You also have a fairly minor alien problem -- the panel's a Murray LC120 and is only listed and labeled for Murray MP breakers as a result. (Newer Siemens/Murray panels are cross-listed for MP and QP, but yours is too old for that.) So, you'll need to replace that BR tandem with a MP2020 and move it to one of the bottom four slots of the panel (as it's currently in a place that violates the panelboard labeling due to CTL issues), while replacing the other BR with a MP120 or an Eaton CL120 (which is UL classified for use in a Murray panel).
Best Answer
You'll have two services there.
As you say, according to PG&E, they design their facilities so that 10KA of short-circuit current is not possible for new single family drops. However, being a duplex with 2 meters, I could imagine them supplying twice the capacity.
That would be 20KA. Since only one service will have a problem at a time, the worst-case assumption is that each service needs to handle that independently.