Usually you can reinstall the apps after you have updated your iPad to the new software version. Just make sure that the app is supported by the new iPadOS system and that you don't throw away any data in apps that you do not have in a backup somewhere. If you're two iPadOS versions behind, make sure that you check any apps that are important to you. The free space after you have updated may be different of course, but you should have something close to the size of the free space now after the process.
Alternative: you can also connect your iPad to a Mac or PC (with the proper software on it) with a USB cable and update through that. In such a case the process will download the update to your Mac or PC (I think) and you don't need to clean up your iPad first. You will still need some spare space on it of course. Worth a try if you have the equipment available.