When I used Online Bill Pay with Wells Fargo some 20 years or more ago it was basically just a GUI for their bill pay system. As such what I did on their site reflected directly into Quicken.
So, with that I would have never "lost my online payees". If I started a new data file and connected it to Wells Fargo it would immediately sync back all the online payees to the Quicken data file. I doubt any of this has changed over the years, so that means I'm guessing that in fact you aren't using Bill Pay through BofA, but instead using Quicken Bill Manger and as such it is certainly not going to know anything about your old online payees. And it isn't going to work anything like the old system because it works with the "billers’ site" not with your financial institution's bill pay system. Note I notice in the most recent versions of Quicken they are calling Online Bill Pay, Bank Bill Pay.
So, you need to make sure that you have setup the account with Direct Connect and Bank Bill Pay, not Express Web Connect and Quicken Bill Manager.
I have been told for BofA the financial institution used needs to be "Bank of America-All Other States" and when you setup the connection to the BofA account to use Direct Connect you probably must use "Advanced Options" to choose Direct Connect.
During the process of creating the new BofA account as a "Connected Account", with Online Bill Pay activated I think BofA will activate Bank Bill Pay automatically.
If not go to the Online Services tab and enable it.
During this connection process your online payees should be updated.