This is almost more of a phone call.
Only the management IP address talks to the cloud to get a config. It also does not use the routing table, just the statically configure default gateway.
Lets take a simple case. If the management IP address is in a VLAN where it can see the device providing Internet access and that is also its default gateway it can simply talk to the Internet to get its config.
Lets take a nastier case. If the management IP default gateway points to the switch itself and then talks to the Internet we can get into a race scenario. The management IP needs the switch up to talk to the Internet, but it can't get the config from the cloud to get the config to bring the switch up. Catch-22.
Lets say you configure up the switch in your lab, and the switch pulls its config. You then go configure its final management IP address so it uses the switch to get to the Internet and put it into production. Now this will actually work - because the switched has already pulled a working configuration. But you are now on a knife edge. If a software update or anything else resets the config then the management ip wont be able to get a config to bring the switch back online, and without the switch online it can't get the config. Catch-22.
The switch that never went down worked because its next hop was another switch.
You should convert the /30 to a /29, and put the management IP and interface IP into this subnet with the default route pointing to the upstream device.