No, the proposed 400A subpanel will not give you more overall capacity. Typically we use 400A subpanels to adhere to the 120% rule. Your main breaker is still the same at 200A.
What it does is allow us to install more generation sources than we are otherwise allowed. Usually we are maxed at total sources = 120% of the buss rating. So a 200A buss has 240A of capacity. If you have a 200A main breaker (Grid Source) then you have 40A left over (PV or PW sources.) If you downsize the main breaker to 150A then you have 90A for PV+PW.
If you use a 200A breaker, and use it to feed a 400A subpanel then you can backfeed up to 200A.
When you say the main bus is maxed out, what are you referring to? You need more physical room for breakers or more electrical capacity for power hungry Teslas? Depending on your utility rules it may be possible to install a different type of main service panel. Maybe a "Solar Ready" 225 A panel with 200A main breaker? These can sometimes be done without replacing the wire from the transformer. However these other panels would only allow you to install more generation sources, you would still be limited to 200A of supply from the utility. This would be "Upgrading the bus." Its much simpler and easier to do these equipment upgrades since you aren't asking PG&E for any more amps.
Increasing the service size from a 200A feed to a 400A feed is doable, but certainly another significant cost. If your feed is underground from the transformer, you may or may not have room in the existing conduit to pull new wire. Most often an underground feed from the transformer means you will need a new trench, wire and conduit. This needs to be done in conjunction with your utility and will usually be 15K+ Replacing the service panel itself with a 400A unit will be 3k to 5k depending on options. If the main feed is overhead you will have to check with your utility. Here in PGE territory, overhead drops are pretty easy to increase in size, and quite cheap or free sometimes, however it will take time, and investigation to see if your transformer has the capacity. This is usually referred to as a "Service Upgrade"