There is no such thing as "W2 contractor."
W2 = Employee
1099-Misc = Independent Contractor and you are running your own business
You can never use another entity's retirement plan if you are not their employee. You seem to be a Subcontractor, contracting through that supplier to the main party having the work done. As their Employee, you would be working for them, and they still are the party contracting to the larger corporation.
QBI has to do with specific expense allowance when you are running your own business. This is not applicable to the employee relationship. As an employee, you would not have expenses against the income; you get Payroll Wages as the income.
Retirement planning can be post-tax funds or pre-tax funds. There can be your own funds, your employer funds, or your own company acts as your "employer" for purposes of funding retirement.
That means there are something like a dozen permutations for what is permitted, and that is something to get personal and direct one-on-one guidance regarding.
You don't get to pick if you want to be 1099-Misc contractor or W2 employee to that other entity, the "supplier." They are supposed to do proper Worker Classification and hire you accordingly, as either one or the other, depending on their circumstances.
