Why are the apps/websites asking to sign in constantly after iPadOS 17.7.7 update?

Multiple reports of issues with iPadOS 17.7.7 have been seen within this Support Community. This release has since been withdrawn by Apple pending release of a new update:

https://www.macrumors.com/2025/05/15/apple-stops-signing-ipados-17-7-7/

You and anyone else that encounter issues subsequent to updating to this version of iPadOS might consider submitting 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; if iPadOS 17.7.7 is not yet listed, choose the nearest from the available options (iPadOS 17.7.6?).

Every Bug Report counts.

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

I hear this a lot after this update. You might want to give this as feedback to apple so that they can look into it and that they know that you're affected as well

Product Feedback - Apple