As described, your Magic Trackpad 2 has a failed battery. All rechargeable batteries have a finite life - and will eventually fail.
To the best of my knowledge, Apple does not offer a battery replacement service for the Magic Trackpad or Magic Mouse. To confirm, 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 you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your device, 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 assist with troubleshooting: