Trying to update an older mac

Here is an Apple article on how to create a bootable macOS USB drive as well as links to download various versions of macOS from 10.11 through 10.15:

https://support.apple.com/en-us/HT201372

Once you have macOS 10.12.6+ installed, then you can take advantage of Internet Recovery Mode as @Johnb-one mentioned and linked.

I highly recommend you have a good backup before upgrading macOS just in case something goes wrong. I also suggest making the bootable macOS USB installer as well as it may prove useful to have if something goes wrong during the upgrade process.

Yes. Maybe try El Capitan or Mojave. Usually older OS updates aren’t available in the App Store, though they might be available if you were to reboot from the recovery partition which you could do by shutting down your MacBook Pro then restarting, holding down the Apple and R keys together. Here’s how to get older Versions of the OS through recovery partition:

https://support.apple.com/en-ca/HT204904

you might find something if you run software update but probably not. Recent stuff tends to not show up there

good luck

John B