The side button does not open the Wallet app. It never has. Double clicking the side button initiates biometric authentication (Face ID). In other words you’re confirming you want to download the app and agree to Apple’s and the app developers terms & conditions. Once you’ve double clicked the download begins. In some countries, regions and US states age confirmation is required by law. This may be what you’re encountering.
These communities are not Apple Support. Apple and Apple Support do not participate in the communities here. They only moderate our posts to insure all user guidelines are followed in regard to content and user behavior. Your comments will not be reviewed by Apple. Everyone posting and commenting are fellow community members trying to assist one another.
You may want to review the articles I linked to so you have a better understanding of what’s required. If not, please contact Apple Support. If you’re in the US, please call 1-800-MY-APPLE, or outside the US, consult the support articles below. In Canada, call 1-800-263-3394.
Contact Apple for support and service - Apple Support