Using my imac (2011) 10.12.6 as a screen for a new mac mini

Target display mode is a feature that was available only with certain older iMac models.

The feature has been deprecated by Apple and is no longer supported in hardware or software.

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

Per the link above:

• Your target iMac (monitor) must be using macOS High Sierra 10.13.6 or earlier. 

• In all cases the source Mac that you're connecting FROM must have been introduced in 2019 or earlier and have macOS 10.15 Catalina or earlier installed.

Your 2011 iMac supports Target Display Mode, using Thunderbolt input. However, Apple added restrictions on the video source. New Macs don't support using any iMac as a Target Display.