First, USB-C cables are fully reversible - and as such, it should make no difference at all to functioning if the connecting plug is reversed. If flipping the plug orientation makes a difference, either the cable or its connector are defective, or the mating device connector has been damaged.
Per your description, the USB-C connector on your iPad may have been damaged, or has an associated fault.
These support pages should help with troubleshooting general battery and charging issues:
Charge and monitor the iPad battery - Apple Support
If your iPad won't charge – Apple Support
Troubleshooting generally requires substitution of the Power Adapter and cable for another known-good item. Most models of iPad require a Power Adapter rated at 12W or greater to reliably charge. 5W Power Adapters intended for older models of iPhone are inadequate to charge an iPad; if the iPad charges at all, charging will be very slow. Recent models of iPad are supplied with a 20W USB-C Power Adapter.
Be aware that many computer USB ports cannot source sufficient power to charge an iPad. Unless explicitly designed for charging connected devices, computer USB ports are typically limited to 0.5-1A @5V (i.e., 2.5-5.0W).
If you continue to experience difficulties when using an appropriate Power Adapter of 12W or greater, you might be best advised to seek assistance directly from from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively, if you have access to another Apple device, 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, Power Adapter and cable(s):
Genius Bar Reservation and Apple Support Options - Apple