For a display monitor for a mac mini 2, can I hook it up to my imac desktop 2019 3.2 GHz 6-core intel i7 on Ventura 13

Not really. Neither the 2019 iMac nor the M2 Mac mini support Target Display Mode.

You can use AirPlay to Mac, but that requires you have a monitor connected to the Mac mini first to set it up. at which point, it's pointless since you already have a monitor you can use.

No. It is a computer, not a display and without Apple's Target Display Mode support. Just buy a 32-in LG 4K HDR display, use a Belkin High-speed HDMI 2.1 cable, and call it a day. That is what I did for my M1 mini and will also use on my ordered M2 mini pro.