Your iPadOS version should be new enough. Screen Mirroring (the video version of AirPlay) is what you are trying to do.
Keep in mind, not all smart TV's support AirPlay. If it's a newer model it probably does, but you should check the TV manual to be sure.
For the menu, go to Setting > Control Center. Make sure Access Within Apps is turned on, otherwise you can only pull the menu down when on a Home Screen. You can also confiture what is in the Control Center here.
Once you pull down the Control Center, tap-hold on a blank area (no control or button) until it goes into edit mode. Choose Add a Control to find and add the Screen Mirroring button. Assuming it is not there.
In iPadOS 18, adding the buttons might still be in the Control Center settings instead of how I just described then. I'm not certain when that changed.