GOTLAND, Sweden—The 150 Swedish soldiers dispatched to this Baltic Sea island for short, routine training last month received an unexpected order: Stay put. The decision made them the country’s first permanent force here in more than a decade.

The deployment is officially a first step to boost Sweden’s homeland defense at a moment when the Baltic Sea has again become a hotbed of East-West tensions, nearly a quarter-century after the downfall of the Soviet Union.

But...