My apologies if a full explanation of the available gestures, ensuring that differences between gestures used for the iPad touch screen and trackpad were understood, missed the mark.
As I sit here using an iPad with a trackpad, I certainly have no difficulty switching between Home Screens using the two-finger swipe gesture (or a single finger with the iPad touch screen). Presumably you are not having other difficulties with swipe gestures - and as such won't have a hardware problem.
If the iPad is not operating as expected, taking a methodical approach to addressing the problem, try a forced-restart of your iPad - as this will often clear an isolated software issue:
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:
- Press and quickly release the volume button nearest to the top button.
- Press and quickly release the volume button farthest from the top button.
- Press and hold the top button.
- When the Apple logo appears, release the top button.
If the problem persists after performing the restart, 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
Should the problem remain unresolved, 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