I’ve successfully integrated all my Matter devices into Apple Home, Aqara, and Home Assistant simultaneously without any stability issues.
There could be several reasons for the instability you’re seeing. I’d recommend checking out my guide for some deeper troubleshooting: Matter & Thread: A Guide Through the Jungle
I would specifically look at the section “Matter Pairing of Devices” → “Connecting to Additional Systems (Multi-Admin)” and the part covering “Link-Local vs. GUA vs. ULA.”