I've never seen the Swiss foreign minister being contradicted by another minister or by an official from a Canton.
But the EU foreign minister can be contradicted by basically any country president/prime minister or their foreign ministers if it says something that is not aligned with every other EU member.
You misunderstood me. If Kaja Kallas says "the EU will do X", then the French or Spanish foreign ministers can say "no, we will not do that". So the EU does not do X because it upset a big country, it will maybe do X-Y or not do it at all if X is dependent on the money spent by France or Spain, or some of their facilities or whatever.
In your example, the mayor can criticize the canton decision, but he cannot do anything about it. That's the difference.