I would like to ask Apple why they didn't add a 'Add Display' feature to Macbook Air (2022). This will allow Macbook Air (2022) to use the old Macbook Pro (early-2015) as a secondary display.
First, you'd have to ask Apple. None of us here work for them.
Second, I told you why as did dialabrain; there is no other device on your network that can host the display. Unless one exists on the network, you won't have any option to add a display. Since you don't have another AirPlay receiver on your network, there isn't an Add Display option. If you add a compatible AirPlay receiver to your Network, then Add Display would be available. Since you don't have a compatible display advertising its services, there is nothing to add.