If the App Store Catalina page says Installed rather than Get or Download then the App Store is detecting that you have got a copy of Install macOS Catalina.app in your Applications folder. Have a look and see if you can find it, it it has downloaded completely it should be 8.24GBs in size. If it is double-click to start the installation.
If it is not then put it in the Trash, and empty the Trash. Connect your mac to your router via cable, restart your mac and try again.
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If you are considering upgrading to Catalina be warned that it does not support 32bit apps.
Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,
some updates may be free, some may be paid. Use this app to discover which apps you have
are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then
contact the developers of the apps to see if they provide 64bit updates.
In theory you can upgrade directly from Mavericks to Catalina but it often stalls
as it tries to convert the HFS+ file system to the new APFS file system.
It is therefore recommended to upgrade to High Sierra beforehand.
Use Safari to click on this link, Firefox will not work.
How to upgrade to macOS High Sierra - Apple Support