ZigBee - Connecting your own device to the manufacturer's gateway

Hello

I would like to connect my own device to a gateway of some manufacturer (and other devices) via ZigBee protocol.
Is this possible due to the incompatibility of the protocol from different manufacturers?
Are the incompatibilities on the hardware or software side?
Does any manufacturer offer an open software or architecture for adapting their own solution to the system?

The second question is whether Zigbee gateways operating offline are cheap to maintain a working schedule for a longer period of time?
What time errors do they generate?

Thank you in advance for your help.

I any device I bought with Zigbee, no matter what manufacturer, could connect and pair with my Raspberry Pi and Conbee USB module.
I didn't have to reprogram the devices (modify the firmware), so it looks like it's not a closed protocol.
However, the gateway was set up on a Raspberry Pi with Conbee and Zigbee2MqttAssistant, all open source and the gateway itself allowed all devices that have Zigbee to connect, regardless of manufacturer.

Eventual limiting can occur on the gateway itself.