I've got a similar problem and unfortunately disabling Bluetooth does not help.
In some apps (those running in a Web Container, i.E. PWAs I have added to home screen) the virtual keyboard stops appearing at some point. Only a reboot will fix it - after which it will appear at first, but it always stops working after a short time. I've tried to disable/enable Scribble because I thought that might be the issue, this makes no difference.
Edit I have the accessibilty dot on screen and that does jump to the top when I focus on an input field. Almost as if the keyboard was popping up, but either behind the container or otherwise not visible
It works fine in most other applications I've tried, i.e. Browsers, Mail etc. It's only in those Web Container apps. (Seen it happen with at least two of these)
I am almost sure this started happening with 14. Am now on 14.4 (iPad Mini 5)
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I've got the same problem - iPadOs 14.0.1 on iPad Mini 5 - keyboard won't pop up in web views from discord or Links added to home page (so, seems to be related to the web view)
Safari and other Browsers, as well as the apps I tried, all works fine. Reboot fixes for a time. Nothing else I've tried so far seemed to help (reduce motion was already disabled, resetting dictionary did nothing either)