It seems the Samsung TV is not compatible with AirPlay as indicated earlier.
If the feature were supported the device name would show up, but the provided image reflects no such connection.
To mirror an iPad wirelessly to a Samsung TV, specialized mirroring apps can be helpful. A suggestion is DoCast. It performs well with Samsung TV and other TV brands, offering more than just mirroring it allows photo and video streaming which often proves more practical.
Other apps worth considering are Screen Mirroring Samsung TV or TV Cast for Samsung TV App. They function effectively but have limited compatibility, primarily with Samsung TV.
An alternative is connecting the iPad using a cable. Read here - https://support.apple.com/en-gb/guide/ipad/ipadf1276cde/ipados
However this method might not be convenient due to the need to stay near the TV while using it.