Where Option Credit gets added

I have a question, when you sell options (call or puts) you get credit upfront, but my question is where you can see these credit amounts? In "Stocks & Options" or in "Brokerage Cash"?

1. When you sell call all your underlying stocks are used as Collateral.
2. When you sell PUT then your cash used as collateral.

I have a question here:

Let’s say you have an account with

Stocks & Options = $20,000.00
Brokerage Cash = $10,000.00

You sold a PUT option and collected $1000.00. So here that $1000.00 with go to Stocks & Options and you can see new value?

Stocks & Options = $21,000.00
Brokerage Cash = $0

2nd Use Case:
Let’s bought the option back before expiry to close the position and paid $200.00 and released the collateral amount ($10,000)
What would be the new Account Value?

Stocks & Options = $21,800.00
Brokerage Cash = $10000.00