Yes, this does appear to be a problem with iPadOS 27/27.0.1 - even after the expected indexing processes (that typically requires several days) have completed. Performance issues, including lagging animation effects and poor/stuttering scrolling, are affecting a wide range of iPad and iPad Pro models.
A forced restart of your iPad may alleviate - but not fully eliminate - the problem:
Force restart iPad - Apple Support
At this time, there is little that you can do other than to report the problem to Apple via its Product Feedback portal - by submitting a Bug Report:
Feedback - iPad - Apple
If submitting a Bug Report, please ensure that you include details of your iPad model and installed version of iPadOS within the body-text of your report. Don't rely upon the pick-list alone - as this rarely includes the current versions.
You would might also report the issue directly from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page.
Alternatively 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