Does Krishna tell Arjuna that you are a kshatriya at the level of a brahmana?
First is that, is there any place where Krishna tells in the Bhagavad Gita that Arjuna, you are a Kshatriya, but your level is of a Brahmana. No, Krishna tells Arjuna very clearly, सभाव जेन कौन्ते निबद्धस लेन कर्ण कर्तुं नेच से मोहात करिश्यस से वश्यो पितत. Krishna says that we are all bound by our nature and we have to act according to our nature.
So Arjuna, you may say, I will not act like a Kshatriya. Kshatriyas are meant to take assertive action. When there is wrongdoing, Kshatriyas are martial guardians of society.
So Kshatriyas are meant to take assertive action, whereas Brahmanas are generally forgiving. So Krishna is telling Arjuna, Arjuna, you think you can act like a Brahmana? You are saying that, oh these Kauravas have abused us, they have stolen our property, I will just forgive them. I will not fight.
Arjuna, you will not be able to sustain action like that. You may think you will act like a Brahmana now, but later on, when a Brahmana goes and asks for charity, the difference between Brahmana and Kshatriya is, a Brahmana takes charity like this. A Kshatriya takes taxes like this.
So he says that when you ask for charity, and if you are not given charity, a Brahmana is tolerant, Brahmana goes to the next person. But when you refuse charity, your hand will go to your bow and arrow. Do you become angry? And Vishwa Chakra Thakur, the Acharya in his commentary, he writes that, at that time when you act like a Kshatriya, after calling yourself a Brahmana, Krishna says, I will come and laugh at you.
Basically, Krishna is saying that, don't act against your nature. Arjuna, you are a Kshatriya, act as a Kshatriya. By acting as a Kshatriya, you will become gradually purified and elevated.
So in 18.41-44, the verses you referred to, they are simply a description of the four Varanas. So he talks about Brahmana, Kshatriya, Vaishya, Shudra, Swabhava, and he uses the characteristics of those. But he does not tell Arjuna, you are a Brahmana.
He tells you, you are at the Kshatriya level. But act on the Kshatriya level, but act with a divine purpose. You cannot, if you are a Kshatriya, you act with the Kshatriya nature, but for a divine purpose, for my service.