Bluetooth keyboard slow-down


I have a brand new iPad Pro 11” running the latest iPadOS. I have been using a Bluetooth keyboard (Apple) for some time now, first on my old iPad Pro 9.7”, now here. For the first time, I start to see a noticeable lag between clicking a key and the character appearing on the screen - after the machine has been running for several hours? Days? I don’t know.

Anyhow, a reboot brings it back to normal. Any ideas why this is happening?
How's the battery level on the keyboard?
When it first started, I assumed the battery was low. So I plugged in a lightning charging cord and left it that way. The new iPad uses USB-C charging. But, after a while, it began lagging again. (Is there a way to check the battery for real?)

So I spent $20 at Walmart for a bluetooth kb powered by 2 AAA’s. But after a while, it too was lagging.
Go to system Preferences>Bluetooth. At the bottom of that panel is Show Bluetooth in menu bar. Click the box. You will see the strange B with a X overlaid on it (the bluetooth icon). When Bluetooth is on you will see three dots across the middle of that icon.
Now when you connect the keyboard you can go to the Bluetooth icon and click and hold. You will see a list of devices that are connected or were connected) select the keyboard and you will get more options. This menu will show you the battery level of the keyboard.