Hi,
To attempt to create a clear and concise question (so most folk don’t TL;DR and move on).
Is your question?:
Can a single Zigbee mesh network have 2x coordinators?
If so, the answer is no.
Two coordinators would fight and break a single mesh, so I don’t understand your Aqara M3 / Homey setup.
There could be two Zigbee RF meshes, with some form of Homey support to control the Aqara M3 (Homey → Matter → M3 → Zigbee → device) as The M3 hub can expose Zigbee devices (and other) devices connected to it via HomeKit / Matter.
ASCII diagram…
/--> Homey Zigbee -> Zigbee Mesh 1 --> device
/
Homey --> Matter --> Aqara M3 Zigbee --> Zigbee mesh 2 --> device
You could create a third mesh network for HA, and gradually move devices from one to the other, but as the multiple meshes would likely be on the same RF frequency, there would likely be interference and poor coverage (which may be happening already…).
Dual-running can work for protocols like MQTT, but typically not RF-protocols, and especially not mesh (which have complex controls).
You can also connect the M3 Hub to HomeAssistant as a Matter device, and control devices (e.g. Zigbee) connected to it indirectly (HA → Matter → M3 → Zigbee → device). This may allow both HA and Homey to control devices paired with the M3 at the same time.
ASCII diagram again…
/--> Homey Zigbee -> Zigbee Mesh 1 --> device
/
Homey --> Matter --> Aqara M3 Zigbee --> Zigbee mesh 2 --> device
/
HA -----/
There seems to be a few ways to connect a Homey to HA, but as that’s not in my experience, try a forum search for the details.
If this helps, 
this post!