I upgraded to 10.15.4 and experienced the same problem.
I have now got Homekit working again.
Take a look at this webpage:
Open a Mac app from an unidentified developerIt took a bit of trial an error but what I did was to disable the HomeKit Bridge plugin and then locate it it in the Plugins (Disabled) folder and then do the CTRL Open as in the instructions above.
You will also need to have the System Preferences > Security & Privacy > General tab open and unlocked. You should then get a message in the bottom to allow it.
It took a few attempts and restarts of the plugin to get it to work.