Start here:
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
…and here:
Recommended settings for Wi-Fi routers and access points - Apple Support
If your WiFi has been set-up according to Apple’s recommended settings, WiFi and Internet connection difficulties are usually an indication that your device does not have a routable IP Address - your IP Address usually being assigned by DHCP. When this occurs, your iPad may only have a self-assigned link-local IP address that begins 169.254.x.x.
If you have a VPN App or profiles installed, or a security App such as Norton, these may be interfering with DHCP and preventing your device from obtaining a valid IP Address for your iPhone hotspot - or the WiFi network to which you are attempting to connect. The resolution is usually simple; if installed, you may only need to temporarily disable or remove the Security App and/or VPN.
DHCP is frequently used to automatically obtain an IP Address. Until your iPad has a valid IP Address to connect to your network, you will not have an internet connection. Disabling or removing VPN and/or the offending security App should allow DHCP to operate normally - allowing connection to your network and the internet.
If this resolves your issue, the VPN and/or security App can be reinstated after the connectivity problem has been resolved.
A further possibility is that you may have iPadOS15 WiFi Private Addressing enabled, this being enabled by default. The WiFi Private Address feature provides additional privacy and security when using “public” (untrusted) WiFi networks. This feature is largely unnecessary for your home WiFi network - and may, in some circumstances, disrupt network connectivity.
This feature is configured for each WiFi network to which you connect. As a diagnostic exercise, try disabling this feature:
Settings > WiFi > [Your Network Name / SSID] - tap the blue “i” icon - Private Wi-Fi Address - set to OFF
More information about this feature can be found here:
Use private Wi-Fi addresses on iPhone, iPad, iPod touch, and Apple Watch - Apple Support