I used 'About This Mac' first, before doing anything, to look at the 'overview' for my MacBook Pro (Retina, 15- inch, mid 2014); macOS Catalina can be installed on this model.
I used Safari to download it ( I entered "How to upgrade macbook pro from macOS High Sierra to macOS Catalina"into Safari browser and clicked on the link https://www.apple.com>mac>macOS
This took me to macOS-How to upgrade-Apple(UG) and apple.com 'Upgrade to macOS Catalina'. I clicked on 'Upgrade now' which connects you to the App store and then I clicked 'Download'.
The download was successful but when I try to 'Open' and 'Install' macOS Catalina the message 'The Recovery Server could not be connected' appears every time I try/retry.
My MacBook Pro is on the list of computers for both macOS Catalina and macOS Big Sur; macOS Catalina needs 4GB of available storage whereas I think macOS Big Sur needs 35.5GB..... Anyway, I have just checked the available storage on my macbook (using 'About This Mac' and 'Storage') and it states that I have '375.4GB available of 500.07GB' so that seems okay (As an aside, the memory for my macbook is 16GB.....Sorry to be so technophobic but I don't really understand where the 500.07GB comes from!?).
The only antivirus installed is Sophos. It was recommended by and installed by the apple store in 2020.
Re your notation on 32/64 bit applications......the Catalina and Big Sur operating systems can be installed on/are compatible with my macbook according to the list provided by Apple.
I wonder if the message could be due to a poor wi fi signal; if so, would it be worth buying a lead to connect my macbook to the ethernet socket in the house (as opposed to trying to do things 'wirelessly')??