200 amp service wire size in Mason County Wa
Apply 310.15(B)(7) to your entire service
NEC 310.15(B)(7)says that you take your entire (planned) service size - 200A - and multiply it by .83 (83%) giving 166A for you. You never need to use wires larger than that anywhere that's served by that service.  So any feeder - even if it's 200A feeder - only needs to be 166A not 200A.
So that calculates out to 4/0 aluminum (180A).  3/0 aluminum is too small to carry 166A.
Footnote:

Now, often when you go shopping for 100A wire, some fool will tell you &quot;oh use #2 aluminum or #4 copper&quot;.  That's wrong.  The person is incorrectly applying 310.15(B)(7) on the assumption that your entire service is 100A, and they don't even realize their blunder because they're just giving 4th generation hand-me-down advice from someone else who misapplied 310.15(B)(7).
Actually, you need #1 Al / #3 Cu for 100A, and 310.15(B)(7) is saying that you never need larger than 4/0 (which isn't very helpful lol).

It's totally OK to oversubscribe
So for instance if you have 200A service, it is OK to have 200A going to the house, 100A going to the shed, 50A to an RV stand, 30A to a well, etc. even though these add up to more than 200A.  That's fine.
You are restricted on how much total load you can have on the service, and this is based on a Load Calculation. But that allows for intermittent and &quot;non-simultaneous use&quot;.  You still want to make each feeder big enough it won't trip on its local loads e.g. welding in the shed with the compressor running.
Consider a &quot;farm panel&quot;
This is a type of service panel that has

Sometimes, a meter
A 200A main breaker
8 breaker spaces (they also make 4-space versions, avoid - too few).
&quot;Thru Lugs&quot; carrying the full 200A onward.

The idea is you come off the &quot;thru lugs&quot; to the biggest load - e.g. the house.  It has access to the full 200A.  Then you use the 8 breaker spaces for four 2-pole &quot;feeder breakers&quot; -- e.g. 50A to the RV stand (they don't need more unless there are two RV stands).  100A to the shop. Etc.
If your existing feeder to the house is only 100A, then go ahead and feed it from one of those four 2-pole brakers, just slap a 100A  breaker in there (90A if the wire is #2 aluminum or #4 copper).
...Except my service is only 100A
Since you expect to go to 200A, I advise still doing the above.
Only difference is you fit a 100A main breaker in the farm panel instead of 200A.  The 200A version of the panel is so popular that cost wise, you are probably better off buying the 200A version of that panel, then buying a retrofit 100A main breaker for it.  Then bag the 200A breaker and leave it in the bottom of the panel for that happy day in the future.