What is the name of the type of bicycle designed for long-distance travel with luggage?

A bicycle designed for long-distance travel with luggage is called a touring bicycle.

Touring bicycles are built for comfort, stability, durability, and carrying weight rather than maximum racing speed. They commonly have mounting points for front and rear racks, panniers, fenders, bottle cages, lights, tools, and spare parts. A longer wheelbase helps create predictable handling and leaves room between the rider’s heels and the luggage.

Compared with a racing road bicycle, a touring bicycle generally uses a more relaxed geometry, stronger wheels, wider tires, and lower gearing for hills while carrying a load. Traditional models often use steel frames because steel is durable and can be repaired relatively easily in remote places, although aluminum and titanium are also used.

“Expedition bike” is a legitimate term for a particularly rugged touring variant intended for rough roads and heavy loads, but it is not the broad category named in the question. Hybrid and commuter bicycles may carry bags, yet they are not specifically defined by long-distance loaded travel.