I have the brother DCP-2540DW printer which worked fine until I updated to 10.15 OS - I installed the latest version from Brother but it is still 32 Bit! Help

The Control Center app is discontinued. They do not have a version for Catalina or later. It is not needed for printing and for scanning use the newer iPrint&Scan app.

Also see the following from Brother: https://help.brother-usa.com/app/answers/detail/a_id/154619/~/controlcenter-is-not-optimized-for-your-mac.

I have a Brother DCP L2540DW and it works with no issues on both Catalina 10.15 and Big Sur 11.

When I upgraded to Catalina 10.15, I downloaded the drivers, the iPrint&Scan Push Scan Tool and the iPrint&Scan application from https://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=dcpl2540dw_us_as&os=10060

When I later upgraded to Big Sur, I didn't need to do anything.

That information is on the Brother site -- but it is pretty well buried there.