Can opening a hotel increase the city's GDP

No, hotel construction has indeed included investment in GDP.

However, the services a person receives when staying in a hotel, the public facilities he uses, etc. There is no statistics, so staying in a hotel will still increase GDP.

This has nothing to do with whether the investment operated by the hotel itself is recovered, because the recovery of investment is the internal behavior of the hotel, and GDP examines the increase of goods or services in the whole country. As long as it is produced by a country within a given time, it should be included in GDP.