Basement underfloor heating or low-temperature radiators

Does anyone have an idea how the underfloor heating works with local or district heating?

Does the water remain in the loop inside my house and only some hot water is added as needed to maintain the temperature?

Basically just like with other heating systems. From the heat generator = for district heating e.g. an incineration plant to the consumer. There, via a separate heat exchanger into your loop. Consumption is then measured via a heat meter at the transfer station. Possibly a second heat exchanger for hot water as well.

With us, there is a combined heat and power plant (CHP) operated by the municipal utilities,

From there, the hot water at 60-80 degrees according to the contract goes to the transfer station, that is clear.

Afterwards, it probably gets mixed with cold water (since the underfloor heating does not run with 60-degree hot water) into the underfloor circuit.

After that, the water stays in the underfloor heating and only new hot water is added as needed?

But the water does not pass through the underfloor heating only once and then get completely replaced by new water?

Did I understand that correctly?

After that, it probably goes mixed with cold water (because the underfloor heating does not run with 60 degrees warm water) into the underfloor circuit.

After that, the water stays in the underfloor heating and only new warm water is added when needed?

But the water does not go through the underfloor heating just once and is then completely replaced by new water?

Did I understand that correctly?

No. Read carefully ;-)
District heating is completely separate from underfloor heating. Heat is transferred via a heat exchanger.

What does that mean? Heat is transferred by heat exchangers? Sorry, I'm too dumb for this :)

The water from the district heating station flows around a coil filled with water and heats it = heat exchanger.