Connecting 2009 IMAC with 2019 IMAC to use as a monitor

Use your iMac as a display with target display mode - Apple Support

It will work if the 2009 iMac is 27". Catalina is OK on the 2019 iMac.

You will need a USB-C to Mini DisplayPort cable,, such as:

https://www.apple.com/shop/product/HN8B2ZM/A/mophie-usb-c-cable-with-mini-displayport-connector

https://www.startech.com/en-us/audio-video-products/cdp2mdpmm1mb

https://www.startech.com/en-us/audio-video-products/cdp2mdpmm6b

Thunderbolt cables and adapters won't work.

While the Late 2009 27" iMac does support Target Display Mode, then new iMac running Catalina does not.

see > https://support.apple.com/en-us/HT204592

Not likely, is the late 2009 a 21.5" or 27".

Your best bet is to buy an external display, iMacs are not intended to be external displays and rather than spending $$ on expensive cables to connect them (even if it works) it make more sense to buy an external display that is much much newer than a 12 year old computer. In addition, external displays have come down in price.

It will work if it’s a 27 inch, I use mine with my 2020 imac which doesn’t have the limitation the thunderbolt target macs do. Use a Mini DisplayPort to thunderbolt 3 cable

https://www.apple.com/shop/product/HN8B2ZM/A/mophie-usb-c-cable-with-mini-displayport-connector

this should work