Sierra to Ventura

Apple says nope.

The following older iMac models can be used as an external display when plugged into another older Mac model.

iMac models introduced in 2011, 2012, 2013, and mid 2014

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Thunderbolt  or Thunderbolt 2  cable.

24-inch and 27-inch iMac models introduced in 2009 and 2010

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Mini DisplayPort  cable.

Yes, setup File Sharing...

Set up file sharing on Mac - Apple Support

Cable solution?

File Sharing can work over Ethernet for one thing.

You're welcvome my friend, post back if you need more help setting it up.

I don't think it's going to slow down either computer much, except of course a bit when files are actually being exchanged, but then may not even be noticeable. :)

OK, take care my friend. :)