2010 imac as a moitor for 2021 mac mini M1

It's a 2020 Mac min.

It has to be a 27" iMac. You need a USB-C to Mini DisplayPort cable, such as:

mophie USB-C Cable with Mini DisplayPort Connector - Apple

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

The "2019 or earlier" doesn't apply with the 2010 iMac since it doesn't use Thunderbolt.

It's the iMac that needs High Sierra or a lower version. Since the 2010 iMac can't run anything later, that's not a problem, Big Sur is fine for the Mac mini.

AFAIK High Sierra or a lower version of MacOS is needed to use an eligible iMac 27" (2009-2013) as an external display. M1 Macs won't be down-gradable to run anything lower than the version of Big Sur it shipped with.

It doesn’t work, all information here is unreliable/hearsay/incomplete.

Here is what a MacRumors post said about using pre TB iMacs (2010 & earlier):

Yes, look at the image I posted - use either #1a or #2 to connect your 2009 iMac to the M1 Mini.

Not holding breath...good luck anyways.