iPad (8th Generation) stuck in recovery mode

Successful past connection is not necessarily a reliable indicator of trouble-free future connection or operation. As such, your assumption may not necessarily be a true reflection of reality.

If your iPad is not being recognised by your computer when connected, try using a different USB port. Otherwise, this support page may be helpful with troubleshooting connection issues:

If your computer doesn't recognize your iPhone, iPad, or iPod - Apple Support

This may also be helpful:

If you can't update or restore your iPad - Apple Support

Assuming that you are connecting to a Windows PC, have you installed iTunes? If not, then your iPad is very unlikely to be recognised by the computer when the iPad is in recovery mode.

If you continue to experience difficulties, you might be best advised to seek assistance directly from from Apple Support. You can contact the Support Team using the Get Support link at top-right of this page. Alternatively, if you have access to another device, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on the device, the App can be downloaded from the App Store:

https://apps.apple.com/gb/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 assist:

Genius Bar Reservation and Apple Support Options - Apple