Why do apps require new login after iPad update to 17.7.7?

Yours is one of many reports of issues with the iPadOS 17.7.7 update seen today. You should submit a Bug Report via Apple's Product Feedback portal.  For iPad and iPadOS:

Feedback - iPad - Apple

When submitting your Bug Report, please ensure that you include details of your iPad model and installed version of iPadOS within the body-text of your report along with details of the problem. Do not rely upon the pick-list - as this rarely includes the current version of iPadOS.

Every Bug Report counts. Unless reports are submitted (with adequate detail), Apple may not assign resources to investigate and correct the issue.

In addition [i.e., not as a substitute] to submitting a Bug Report, you might also consider seeking assistance directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page; you can initiate and manage your support cases from Apple devices using the excellent Apple Support App. If not already installed, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

iPadOS 17.7.8 has been released - and is now available for download.