A Light Sport Aircraft pilot reported on landing roll they observed an Air Carrier departing from an intersecting runway and braked immediately to stop prior to the intersection.

Narrative

I conducted a discovery flight. After departing ZZZ; we proceeded northbound toward ZZZ1 for the initial portion of the flight. Upon completion of the sightseeing segment; I contacted ZZZ Tower to request re-entry into the airspace and advised that we were ready to return to the airport.Tower instructed us to expect a left downwind entry for Runway XX and advised us to extend our downwind. After repeating the instructions we complied and extended the downwind leg; I was instructed to turn base and cleared to land on Runway XX. I read back the landing clearance as issued. While established on final; the tower advised me to slow down for traffic departing on an intersecting runway. I reduced speed accordingly.Subsequently; I was instructed to make a small S-turn for spacing; I read back the instruction and promptly executed the maneuver. Tower then stated; 'Aircraft X; spacing looks good; Runway XX cleared to land.' I repeated the clearance and continued the approach to landing.After a successful touchdown on Runway XX I started to apply the brakes to reduce my landing roll and ground speed; however to my surprise when approaching the runway intersection; both my passenger and I observed Aircraft Y commencing takeoff roll on the intersecting runway directly ahead of us. No Land and Hold Short (LAHSO) clearance was issued to us at any point during the approach or landing sequence. Recognizing the potential conflict; I applied full brakes to come to a complete stop before the runway intersection and avoid any incursion.Thereafter; tower transmitted; 'Aircraft X stop.' I remained stopped on the runway until the tower instructed us to taxi full length and contact ground. Ground then provided taxi instructions for our return to the ramp; and we exited the runway uneventfully.Remarks: The situation could have resulted in a runway incursion or worse had we not acted promptly.