How do I access apps getting ‘Needs to be updated’ message?

Unless you are able to download and install the App from the App Store, any data associated with the App is inaccessible. When Apps are abandoned or withdrawn by the App Developer, unless data is accessibly backed-up elsewhere, data loss will occur.

You will need to seek assistance from the respective App Developer(s):

How to contact an app developer – Apple Support

Your raw data already needs to have been backed-up elsewhere - in an accessible form - if you are to be able to make use of it.

Your iPad still has a copy of the [now inaccessible] App data for the Apps that you now cannot install - and will continue to do so until it is deleted.