Talk about timetravelling 😉 So the while the management of the core switches itself is separate from the routing that it provides for downstream devices the limitation is that you cannot use the routing of the core switch to route it's own management traffic. So in case you want to use the same subnet for management of the core as it's own uplink you need to have that subnet large enough so it fits both upstream ISP router IP(s) the core stack SVI AND the management IP's of both stackmembers. And yes the router of the ISP is then the default gateway for the management of the core switch. About the switch settings page. You are welcome to enter a VLAN ID there which will become the default for all the MS switches in the same network that DO NOT have a VLAN ID configured on their own management settings. So you could enter for example VLAN 100 as management that has an SVI on the core switch to route the downstream switch mgmt while having a different VLAN ID on the core switches themselves by entering the VLAN ID individually on both core switch mgmt IP.
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