Hi!
No, unfortunately, Apple didn’t create a password feature on an iPhone app. However there is one method that doesn’t even require third-party apps or websites. In fact, Apple has created a pre-installed app on each of its devices: Shortcuts. This app allows you to create quick commands to control your device. I created a quick command for you to protect an app of your choice on your iPhone. Here is the download link: https://www.icloud.com/shortcuts/19e3b21dc2cd496b95664687889662ee. All you have to do is open the link and press the "Get" button below. After you do this, the Shortcuts app will open and you will need to press "Add" at the bottom. At this point press on the three dots next to the name "Password" and the icon of a white cube. Now a screen will open. You have to put the password you want instead of the default one that I put, "1234", in the box with the words "If" flanked by two divergent arrows. Immediately after you have to press on "App" next to "Open" and choose the app you want to open if the password is correct. Now the final part is missing: search the internet or take a screenshot of the app icon you want to open and save it to Photos. Now go back to Shortcuts, open the quick command "Password" if you closed it and press the share key at the bottom (the one with a square and an arrow). Now go down and press "Add to Home Screen". At this point enter the app name instead of "Password" and press on the icon of the next white cube (the one below). Now press "Choose photo", select the app icon, center it in the square and press "Choose" at the bottom. Then press "Add" at the top. The last thing you need to do is go to the Home screen, search for the location of the original app you want to enter the password, press on long press, press on "Remove app" and press on the blue "Remove from Home screen". Finally, locate the quick command on the Home screen and move it wherever you want.
I hope I helped you and I hope you enjoy your new iPhone 13!