Old Mac used as second monitor

+1 on Servant's advice. The 21.5-inch iMacs in 2009 never supported Target Display Mode (TDM).

TDM was very limited, and neither of your devices is supported. See the restrictive TDM hardware and OS restrictions in this Apple article:

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

Apple started the deprecation of Target Display Mode in late 2014 and threw the last shovel of dirt in its face in Early 2020.

• Astropad says that Luna Display is "NOT recommended for gaming, video playback, or other high-motion content." So it's not quite as good as a using a dedicated monitor.
• If you're in the market for a budget monitor, look for one with an IPS panel, modern video input ports, and near-100% coverage of sRGB. Standard resolution for a budget 24" monitor is 1920x1080 or 1920x1200 pixels; for a budget 27" monitor, it is 2560x1440 pixels.
• You can get 27" 2560x1440 monitors with very good specifications (including good coverage of DCI-P3) pretty cheap now. Dell has one for $315 and Asus has one for $350. Much better than $1,200 (the price which you would have paid for a 27" 2.5K monitor around the time the Late 2009 iMacs were released).

Servant of Cats wrote:

• Astropad says that Luna Display is "NOT recommended for gaming, video playback, or other high-motion content." So it's not quite as good as a using a dedicated monitor.

Which is why I said it makes more sense to use a monitor. lol

Not to mention there are oodles of 1920x1080 monitors for under $200.

Even if your Late 2009 iMac was a 27” one that supports Target Display Mode, your new Mac could not use it as a TDM monitor.

You might be able to use Luna Display but, since it costs almost as much as a reasonably priced 27" monitor with better resolution, it makes more sense to get a monitor.