iPad keyboard stays up for a second even when messages swiped away

This behaviour that you describe - with the on-screen keyboard remaining on the screen for a few seconds - is a bug in iPadOS 27.

You and anyone else that encounters this issue would be best advised to submit a Bug Report via Apple's Product Feedback portal:

Feedback - Apple

When submitting your Bug Report, please ensure that you include details of your device model and installed OS versions within the body-text of your report along with details of the problem.  Do not rely upon the pick-list alone - as this often fails to include the most recent OS versions.

Every Bug Report counts. Unless sufficient 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

I suggest that you put your iPads on charge for at least half an hour, then, keeping them plugged in, try a "forced" restart using these instructions:

• On an iPad with a Home button: Press and hold the power button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: In rapid sequence, press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the power button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

If the issue persists, contact Apple Support directly, using this link:--> Contact - Official Apple Support

Regards

Giulio

Yes, you would be well advised to submit a bug report as described. If nobody submits a report, nobody at Apple will have any cause to investigate and resolve the problem.

Thanks for update! I started off with call to Apple Support and was told by the AI that there hadn't been any reports of this issue with iPadOS27... so I did send in a bug report with all the info...