Whose gas is consumed for indirect contract's function call?

i'm working on solidity for Dapp dev.

Let me assume this situation below, with 2 contracts, A and B.

contract A {
    B contract_b;
    constructor(address b_addr) {
        contract_b = B(b_addr);
    }

    function pass() public {
        contract_b.do_sth();
    }
}

contract B {
    constructor(address b_addr) {
        //
    }

    function do_sth() external {
        // do something state-changing stuffs //
    }
}

I vaguely noticed that view function does not spend gas,

so if do_sth() is view function, then nothings' bothering.

but with debugging, i found that in processing do_sth() invoked by pass(),

msg.sender becomes the constact address of A, not the original sender.

which means, in do_sth() scope, msg.sender is changed.

Then, whose gas will be consumed for do_sth() process?