I am also having this problem with an Ipad Pro 2018 running on the latest iPadOS version and it is very frustrating!
I have 2 bluetooth keyboards, both working fine with my Iphone 8 as well as with my iPad Air 2 (sold in the meantime, before updating to iPadOS).
With the Ipad Pro it is always a problem, sometimes they works, but mostly not (sometimes with huge lag, sometimes not at all). I tried rebooting the ipad, installing/de-installing the keyboards, erasing the networks settings and also run a software check (with no errors found), but nothing seems to help. It seems that the ipad or the ipadOS has general connectivity problems which are not been addressed correctly making the experience quite poor. I mean, connectivity is key in 2019!
Please solve this problem because it makes impossible to use the ipad as a serious working tool!
I am super fed up with all the recent issues as I am loosing a lot of productive time! I am seriously considering switching to another platform.