another train which connects me to Warsaw Chopin Airport
Trains to the airport go from Warszawa Centralna at the moment. They also usually stop at Warszawa Zachodnia and often Warszawa Wschodnia and although Wschodnia is the most user friendly, it's the furthest from the airport. Centralna is larger and closer to the airport. If you buy a ticket from Gdańsk to the airport, the website will make it clear where you change.
Worth mentioning that there are major building works and Centralna is connected to Śródmieście Station or was when I last travelled by train there a few weeks back. If this is still happening when you travel, you will know about it when you buy your ticket and any changes shouldn't inconvenience you.
Alternatively, a taxi from outside any of the main stations in Warsaw to the airport is not expensive. The cheapest journey there by taxi is from Zachodnia however that station is a nuisance if you have heavy luggage or mobility issues.