iMac 27" mid-2011 Airdrop does not work

You can easily setup both File Sharing and Screen Sharing over your local network.

see > https://support.apple.com/guide/mac-help/use-file-sharing-mh17131/10.13/mac/10.13

and > https://support.apple.com/guide/mac-help/set-up-and-use-screen-sharing-mh11848/10.13/mac/10.13

FWIW I use File and Screen Sharing between several 2010-2012 Mac's and it work quite well for sharing files and controlling my headless 2011 Mac Mini media server.

Air Drop only works with 2012 and later iMac's.

see > https://support.apple.com/en-us/HT203106

What other devices are you trying to share files with?

You're welcome.