Correct. When a unionized employer enters into a new contract, on or after November 21, 2020, the notice that unionized employers are required to send to their unions and post "in conspicuous places" is supposed to come from the government agency with which you are contracting. The Executive Order did not contain a requirement for non-unionized employers to put up any notice. If you a unionized employer, have entered into a new contract, and don't have the notice from your contracting officer, and the union is not pressing you to put up the notice, perhaps you might consider waiting a month or so, after the inauguration, and see how this plays out.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.