I just went through a few days of trying to connect Hubitat to the ESP32 C6 using the Arduino IDE. All attempts failed. Then I finally asked an AI program the question "Is it possible" and it said No.
The Hubitat Zigbee has been great with off the shelf products, I have about 18 Zigbee devices connected to my Hubitat.
I am not sure if it is Hubitats problem or a quirk with the ESP32 but Home Assistant connects to the ESP32 Zigbee so Hubitat should also connect?
You can use MakerAPI and connect Arduino's/ESP32's. I have some of each. There are other ways besides MakerAPI.
I never tried Zigbee, but I did get Thread working on a -C6:
It's just a template really.. of a "Dimmer" because I got the new C8-Pro T hub. It works with a built-in Generic Matter Dimmer driver. I'm surprised it doesn't work with Zigbee. (Matter is on all my hubs, Thread on only one hub. Zigbee is on just one hub too.)
Note: I only use ESP-IDF for these projects.
Some people have gotten it working:
There is/was a fairly long discussion shortly after they first came out that had some success after a LOT of effort working through a bunch of gotchas and such.