What you want to know is whether you have the address in your wallet. I'm not sure that a search function is necessarily the way to go, you don't want to search for it since you already have it, you just want to know if it is in your wallet. You can do that right now using the debug console with the validateaddress command. Just do validateaddress <address> and in the output you will see something that says ismine. If the address is yours and you have the private key, that field will say true.
Yeah, like I said im aware that you can do these things with the console command, you can pretty much do anything with cvars, but how can we get more people to use Bitcoin Core if we don't make the GUI better? most people are too scared to use debug consoles. If we want to establish a culture where everyone runs a node, we need to make the GUI as user friendly as possible.
Also, what I think would make everyone run a node is if we somehow managed to not need to download the entire blockchain at first boot to run pruned mode. Sure having the full blockchain is better, but if we could get the people that use Electrum to download 1 GB to run bitcoin core, the node count would skyrocket. Too bad this seems somehow impossible at least for now. Maybe in the future some genius comes up with a way to do it.