2011imac Catalina to 2015imac Monteray 5k Thunder bolt screen conect

It sounds like you are trying to use a 2011 iMac running Catalina as a screen for a Mac mini running Monterey and are discovering that this isn't going to work.

You mention having a Thunderbolt cable. 2011 iMacs can support Target Display Mode using Thunderbolt input. Unfortunately for you, your configuration does not satisfy the very restrictive requirements set forth in Use your iMac as a display with target display mode - Apple Support .

• Your iMac is running Catalina. That's not supported. To put it into Target Display Mode, you would need it to start up from a drive using High Sierra or earlier.
• Your Mac mini is running Monterey. That's not supported. If you wanted to use an iMac as a Target Display, you'd need to start up your Mac mini from a drive using Catalina or earlier (assuming ti can run Catalina).

Also,

• I don't believe that you need to set up a Thunderbolt Bridge to use Thunderbolt Target Display Mode. You'd configure a Thunderbolt Bridge if you wanted to use Thunderbolt to network two Macs (Ethernet-style).
• You haven't told us which Mac mini you have. If it is any of the ones with an Apple Silicon (M-series) chip, it would be too new to support using ANY iMac as a Target Display.

on YouTube the guy is using a laptop and his is found in the add display drop down but I don't have an add display drop down just and air play which is located on the other side.

That sounds like someone doing AirPlay from one Mac to another using AirPlay to Mac. AirPlay is a lower-quality connection method. Even your 2011 iMac should be able to AirPlay to an Apple TV set-top box, but a 2011 iMac would be way too old to act as an AirPlay Receiver for AirPlay to Mac.

Continuity features and requirements for Apple devices - Apple Support

To support being an AirPlay Receiver, that iMac would need to be from 2019 or later – and be running Monterey or later.

Note that if you were trying to go in the other direction, the 2015 iMac does not support being a Target Display at all. Target Display Mode went away when the first 27" 5K Retina iMac came out in Late 2014, and never returned.