how to update OSCatalina to new OS

Back up your data, check the application compatibility table, click here, and if your iMac is a 2014 or newer model, then on the download link for a higher OS. Alternatively, use a different web browser as needed.

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Use Time Machine to create a backup of the data on your 2009 iMac.

Back up your Mac with Time Machine - Apple Support

The new Mac may already have a much newer macOS version installed, so you will restore your user data, files and folders from the backup drive to the new Mac.

If you happen to buy a 2019 mac that still has macOS 10.15 Catalina installed, you can of course proceed to upgrade that to a newer macOS version... probably even up to macOS 14 Sonoma. In which case, you will still use the backup that you create with the old iMac to move you stuff onto the new.

Ethernet file transfer between Macs is doable with file sharing setup, but the process is cumbersome and not really suited to this task.

Use Ethernet to connect two Mac computers - Apple Support

I advise that if you decide to replace your current machine, you would be doing yourself a great favor if you also get an external drive. You will use that to create a backup of the old Mac, then transfer those files to the new. After that, you'll continue to use the external drive to backup the new Mac and now have the ability to better resolve any problems you might have in the future.

Having no backups of your data is a promise that you will lose that data... it's just a matter of time.

If your Mac does not qualify to run an upgraded version of macOS, and if you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.

I suggest you take a look at Firefox browser or Brave browser... or even Chrome 🙄.

The Safari browser is typically updated with a macOS update or upgrade. Of course, that only happens if your Mac can support the newer macOS version.

My early 2009 iMac won’t update,If I get a late 2019 iMac will it update from High Sierra to newest version when I transfer all my data from my old iMac?

How about Ethernet to Ethernet from the start up disk from my old computer