Okay your iMac from 2013 can upgrade as far as macOS Catalina 10.15.7.
You tried to install Sierra, this downloads as InstallOS.dmg and you opened that to get the InstallOS.pkg.
On opening that you would have got an installation window.
This does not install macOS Sierra but creates the Install macOS Sierra.app which you will find in your Applications folder,
have a look. Double-click on that to install macOS Sierra.
If you want to upgrade to Mojave or Catalina I would upgrade to macOS High Sierra first.
Follow the instructions carefully below, read everything.
For High Sierra, Mojave, Catalina,
Open Safari and click on this link,
How to get older versions of macOS
Go to the Use Safari to download macOS section and click on the OS you want to install.
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.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If the App Store says ‘Open’ then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS ******.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.
If you are considering upgrading to Catalina be warned 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 free app to discover which apps you have
are 32bit, https://www.stclairsoft.com/Go64/ then contact the developers of the software to see
if they are offering 64bit updates.