In environments like this, my trusted colleagues and I communicated using Signal (and before that, WhatsApp).
One somewhat paranoid department that was convinced they were being spied on (they weren’t; I saw the Slack admin dashboard and management was too cheap to pay for the retention and spying features) maintained the use of an ancient Jabber based group chat for their own internal communications.
This was around 8 years ago, but there was no MDM installed on our cell phones, regardless of if BYOB or company paid for device.
The only restriction was if you went to China, you took a burner phone (one of the old company phones, usually) and weren’t supposed to ever use it again once you left. I think they just sold them to a liquidator.