improvedFunction.ts

function createInvoice(client, user): void {
    validate(user);
    validate(client);
    const userPermission = await callApi2(user) // I would keep this sepparate because it should be much faster then rest and can avoid unnecessary calls (if permissions fails)
    if (validatePermission(userPermission)) {
        throw exception;
    }

    const [invoiceData, orders] = await Promise.all([ // we can call this in parraller
        callApi2(user),
        callApi3(client)
    ])

    const provision = calculateProvision(client);
    const invoice = generateInvoce(client, ordes, user, provision); // can (and should) be immutable also all calculations which does not requiere dependecies can be encapsulated

    return invoice;
}