Updating Late 2009 iMac

I always update old Macs to the latest macOS they support (and install Firefox 78.15.0esr as a browser because old Safari might not work anymore). And optionally replace the internal HDD with a much faster SSD, if possible and financially reasonable (or just use an external boot SSD).

I'd make a bootable clone of the internal disk to an external disk with some old Carbon Copy Cloner version and verify it boots.

Then maybe try to install (or upgrade to) High Sierra to another external disk (or partition). Just in case to check that it works.

Then clone (or install) High Sierra on the internal HDD (or SSD).

I guess that should be a safe workflow.

I would upgrade it. my previous iMac was also the late 2009 model. it ran beautifully on High Sierra. and FWIW, when I retired it, I gifted it to my dad to replace his even more outdated MacBook. he loves it. and he appreciates the extra real estate of the 21.5 inch display. his MacBook was only 13 inches.

just please make a backup before upgrading if you have any data you are not prepared to lose. the upgrade should go smoothly, but it's better to be safe than sorry.

That 2009 iMac is fifteen (!) years old and well obsolete. Your concern that an upgrade to a newer OS -one that is also obsolete- might render it laggy or inoperable is valid, but you should be more concerned about how much longer you can nurse it along.

You would do well to find a newer Mac to move forward with. A quality iMac half its age can be purchased for only a few hundred dollars. Just sayin'.

New, Used and Refurbished Macs - eshop.macsales.com (unaffiliated)

Refurbished Mac Deals - Apple (also unaffiliated)

You can get macOS installers here.

How to download and install macOS - Apple Support

When using an App Store link (like the one for High Sierra), it's a good idea to be running Safari and have Safari set as your default Web browser. Other Web browsers may return incorrect and extremely misleading errors (e.g., "the item you requested is not available in the U.S. App Store").

Once the machine is running High Sierra, you can install Firefox 115 ESR.

https://support.mozilla.org/en-US/kb/firefox-users-macos-1012-1013-1014-moving-to-extended-support

it depends on which macOS the Mac is currently using. I would suggest upgrading one macOS at a time. I have seen instances where the user encounters issues while skipping over some macOSes. I personally have never lost data, nor experienced issues due to an upgrade.

and also, it is a rare occurrence for issues to arise due to a macOS upgrade. but you should make a backup anyways.