We have a 2009 iMac here, not identical to you but very similar vintage. After running through a battery of Linux distros on it (I'm a bit of an operating system nerd) I found that Ubuntu/Mint have the best hardware support for old Mac's.
Being told to try Debian on Mac's of this vintage is not helpful in my experience. No disrespect to Debian.
Your spinning rust will run Linux better than MacOS in terms of performance and resource use.
Installing an SSD running Linux will do wonders with old Mac hardware with the caveat that Apple's firmware will maliciously set the system fans to full blast for the sin of using a non Apple SSD.
The fan issue is easily fixed with a small bit of software which over rides Apple's firmware to set the fans back to normal speeds.
As a bonus, if you'd like to get rid of the loud Apple 'bong' at startup there is a way to do it in Linux.
3gb of ram is always going to deliver a sub par experience. Set your limit at phones with 4gb ram as a minimum.
Having said that, Motorola has traditionally done a lot with the available ram on their devices, its just that Android is becoming more ram hungry with each successive iteration.
I have a 2009 iMac (Intel Core 2 Duo, 4mb RAM) sitting here that needed even lighter. I found Bodhi 6.0 booted its full graphical desktop (Moksha, a fork of Enlightenment) in 250Mb of RAM. Not a typo. I was so impressed at how zippy it was I installed it on an old HP Pavilion G6 laptop (Core i3, 4mb RAM, SSD) and it positively flies.
Disk caching only benefits spinning rust.
Operating from solid state storage such as SSD or NVME pointlessly wastes CPU/RAM resources juggling memory.
I turn all this archaic nonsense off (as far as I can) when running solid state media.