Can I use a 2012 iMac running macOS Catalina 10.15.7 as a monitor for a new Mac mini?

No. Even if you downgraded the 2012 iMac to High Sierra, and purchased the $80+ of specialized hardware (Apple Thunderbolt 3-to-2 adapter + a Thunderbolt 1/2 cable) needed to make a Thunderbolt connection, there would still be a deal-killer.

No current or recent Mac supports using any iMac as a Target Display.

Nope' you need an external Monitor/Display or HDMI TV for the Mac mini.

see > Connect a display to Mac mini - Apple Support

This Apple article shows why you cannot:

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

specifically:

There is not a true hardware option to connect the two computers as an external display, in the traditional sense.

There is a software option, depending on the speed of your local network, which might be suitable for some purposes, using VNC software. Check out RealVNC or TightVNC to see if that might be a workable option. There may be some laggy performance in the GUI, like if you are running high-end 3D games, CAD, or video editing software, where this might not be workable. Email, web browsing, and simple word processing, probably works fine. Easy enough to try and see if it works for your needs. Best to have a dedicated monitor on the Mac mini, but maybe can use a smaller cheaper one, and when you want to have a larger desktop, connect via VNC from the iMac, as one hypothetical scenario.

Apple Remote Desktop is another $ option.

No.

+1 Nope! iMacs are computers, they are not external displays for other devices.