CustomeContactLabelProblem,
Thank you for that helpful information. Deleting the Contacts app on your iPad Air 2 shouldn't have affected that option to add a customer label. Since you're still unable to add a customer label with iOS 15 after those steps, you can contact Apple Support for further assistance here: Contact Apple Support
As for the other issue you mentioned, you did the right steps closing that website and the app, as it wasn't legitimate. Check out the information below, from the following article, which has some more information that should be helpful: Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support
While browsing the web, if you see a pop-up or alert that offers you a free prize or warns you about security problems or viruses on your device, don't believe it. These types of pop-ups are usually fraudulent advertisements, designed to trick you into downloading damaging software or giving the scammer personal information or money.
Don't call the number or follow the links to claim the prize or fix the problem. Ignore the message and simply navigate away from the page or close the entire window or tab.
Use extreme caution if you download content from the internet. Some downloads found on the internet may not contain the software they claim to, or may contain software that you didn't expect or want. This includes apps that ask to install configuration profiles that can then control your device. If installed, unknown or unwanted software may become intrusive and annoying and could even damage your Mac and steal your data.
To avoid unwanted, fake, or malicious software, install software from the App Store or get it directly from the developer's website. Learn how to safely open software on your Mac or remove unwanted configuration profiles from your iPhone, iPad, or iPod touch."
This article shows how to stop pop-up ads, which might help: About pop-up ads and windows in Safari - Apple Support
Take care.