For recording usage you don't add up your breakers as not all loads are continuous. There is a giant formula on how to factor in loads compared to main service to be under 80% listed in NEC (I will try and find it)

The backfed breaker serves three purposes.

1)To feed the inverter in order to charge batteries. That would be this section:

If you charged at a continuous 185 amps DC (48v but the charge voltage would be around 56v) that would put you at 10360 watts.

Convert that from DC to AC with losses would get you around 40 amps at 240v. 1.2x of that would be 48 amps.

2)To be fed by the inverter to power the main panel. That would be this section:

The inverter can only push a max of 9000 watts AC to the Main panel at a maximum of 37.5 amps. 1.2x of that would be 45 amps.

3)To feed power to the critical loads panel directly through the inverter (Passthrough). That would be this section:

Hypothetically you can passthrough as much power as your wiring and breaker and CLP can take but we are limited to 63 amps internally of the Sol-Ark in which that power is passing through. Since that is the max amp before the breaker triggers we would want 63 amps to be our 1.2x number so we divide 63 by 1.2(instead of multiply) to get 52.5 amps. 52.5 amps would be our maximum load for continuous operation.

Now that we have all 3 of these numbers we see which parts apply to you and use the largest amperage that does.Perhaps you're not charging a battery or doing AC passthrough to a CLP (I don't have a CLP)

In your situation passthrough is your highest amperage at 52.5 amps so you would use the next up breaker of that and wire that supports that breakers size in this case 60 amp breaker and wire that supports 60 amps (4awg is good)

Derating only applies when we are pushing power to the panel not pulling so we would use the numbers for the inverter at 45 amps. You already have a 60 amp breaker for passthrough so you are covered but you need to derate as 200 amps x 1.2 ='s 240 and you need 245. Some AHJ's don't care about the actual wattage of the device putting in and only look at the capacity for derating so by having that 60 amp breaker they expect you to have account for that 60 amps (Instead of just 45) on the panel. Either way the next step down for a main breaker is 175 amps which frees up 25 amps from service and you still have the 40 extra you are allowed for a total of 65 amps of capacity.

Short version.

Derate to 175 and keep your 60 amp breaker.