This is a heritage from an old friend of mine who died in 2011 (so the OS and apps are outdated) and I don't have the money for another iMac (the Air I recently bought for 20€ was broken and I decided to fix it)
I've been using iMac 2009 with High Sierra until recently (actually it's my 13yr son who is using it.)
On Mac OS High Sierra, the following Apps work well:
Microsoft Edge
Google Chrome
Safari (if you insist on using Apple app)
MS Office 2011 (or 2012, not quite remember); before that I used Libre Office with no issue, just some inconvenience due to my familiarity with MS Office.
For gaming, the HD4850 500MB in iMac 2009 is not enough in every aspect. I upgraded to Quadro K1100m, some web-base games still worked, but very laggy.
Gaming experience has improved a lot since I upgraded the GPU to Quadro M4000m 4GB. (quite pricey)
Now I have removed the Quadro M4000m to install to iMac 2011; leaving my son's iMac with the cheap AMD Firepro M6100 2GB (cheap and affordable). The OS has been upgraded to Monterey using OCLP, MS Office 365. The general experience is quite good. My son doesn't play game much, he watches Youtube most of his online time.
So for your iMac 2009, I would suggest you spend some money for a better usage experience and convenience.
First thing first, upgrade your iMac OS to the latest version of High Sierra and get the firmware updated to the latest version in the process (mostly for APFS format to be recognizable and usable)
1. Replace the internal disk with SSD (256GB is nearly enough, 512GB is enough for light use)
2. Increase RAM to 16GB (2nd DDR3 SODIMM are dirt cheap now, around 8USD per 8GB stick where I live). You can go with 4x4GB or 2x8GB, depending on how you can source for them in your neighborhood, sometimes you can get them for free from the local laptop repair shop.
3. With OCLP, you can upgrade the Mac OS to much recent version, like Monterey, Venture or even Sequoia. Check OCLP website for supported GPU.