There's a possibility: Philips upgraded the Hub firmware on May 1st. It seems that this is where problems started with HomeKit connection.
Same symptoms: Hue apps and all devices work, but no HomeKit connection. In the hue app/settings/voice companion/homekit, I'm asked to reconnect to the hub to activate HomeKit by pressing on the hub button, but Hue app doesn't detect when I press it and remains "searching", so I'm unable to reconnect.
I didn't want to reset my hub yet (dozens of devices to reconfigure...).
Tweethue has been saying "we are aware of the issue and looking for a fix" but it has now been 17 days...
Interestingly, I have 2 homes: one is still working perfectly (the "main" home in Hue app, accessible from internet) and the other one is failing. So it is not a general bug.