My brand-new iPad pro m5 says it isn’t connected to the internet, but it is…

Did you already check, if those apps are allowed Wi-Fi access in the settings for Privacy & Security?

Have a look at this article:

If an app would like to connect to devices on your local network - Apple Support

If the problem persists, it may be necessary to reset your iPad settings. While this reset will not cause any loss of data, as a precaution, it is always wise to ensure that you have a current iCloud or iTunes backup before performing the reset:

How to back up your iPhone, iPad, and iPod touch - Apple Support

When you are happy to proceed, you can perform the reset from iPad settings:

Settings > General > Transfer or Reset iPad > Reset > Reset All Settings

If the problem still doesn’t clear, the next step is to reset the iPad to factory settings:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Otherwise, you would be best advised to seek assistance directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively and perhaps easier, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad - and you can explore your available options:

Genius Bar Reservation and Apple Support Options - Apple

If you have a VPN App or profiles installed, or a security/AV/firewall App such as Norton, these may be interfering with your iPad's network stack. If applicable, the resolution is usually simple; if installed, you may need to temporarily disable or completely remove the Security App and/or VPN.

If this resolves your issue, the VPN and/or security App can be reinstated after the connectivity problem has been resolved.

If some Apps are working as expected, while others are not - or other devices can connect to your WiFi network - you may find that a restart of your WiFi Router, followed by a restart of your iPad will clear the problem….

To restart your router, disconnect power from the router for at least 30 seconds - then reconnect power to restart. After your router reboots (which may take several minutes), force restart your iPad:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

If you continue to have difficulties, check to see if your iPad is using the WiFi Private Address feature. This feature is intended to provide additional privacy and security when using “public” (untrusted) WiFi networks.

Settings > WiFi > [Your WiFi Network / SSID] - tap the “i” icon - Private Address

The Private Address feature is largely unnecessary for your home WiFi network; if enabled, Private Addressing can cause issues if specific MAC addresses are expected by your WiFi Router. You may need to disable this feature - and can be enabled or disabled for each individual network.

Use private Wi-Fi addresses in iOS 14, iPadOS 14, and watchOS 7 - Apple Support

I'm delighted that you had a great experience with Apple and its staff. While everyone is different (would life be bland is everyone were cloned), my own experiences with Apple staff has been much like you own.

Am delighted to learn that your problem has been resolved. Sometimes simply engaging with an Apple technician - and working through the problem - is inexplicably all that it takes... 🙂