That includes the cost of mining without which your computer would not be able to verify the transaction.
New blocks are created with transactions in them and can’t be verified if they haven’t been mined, because verification works by checking the hash that the miner found.
Transactions that are not yet part of a mined block cannot be verified.
So paying the cost of mining is a prerequisite for verification.
You can definitely separate out the costs, but it’s misleading to imply that mining isn’t a requirement and that you also have to pay that cost first.
And a statement like this…
> The mining is not needed at all for verifying transactions, it is used to secure the network and to create new block of transactions.
…isn’t correct - mining is needed for verification. You cannot have verification of new transactions without mining.