Okay here is my theory about how the dragon, samurai, marines and world government are related in this arc.
Here goes. The dragon race who had live in isolation for hundreds of years until humans (mostly the samurai of the wano country and marines) saught to eliminate them because of the threat they posed was once had a fair amount of members. The dragon in the current plot is one of the few surviving dragons and it decided to take revenge for it's fallen comrades and started to attack humans (mostly world government bases and villages and towns of the wano country). After destroying multiple government bases and villages the dragon came across a marine base which was distant from other islands (Punk Hazard) which was a winter islands after defeating the marines it decided to make this base its domain and began to burn the island with flames strong enough to burn the seas to make the island more to its liking. Due to this the government had to seal the island off from the public. The dragon continued its rampage of vengance on the government and wano country. The wano country became infuriated due to the dragons actions and secretly requested permision from the government to send a few select samurai to slay the dragon the government agreed because the samurai of the wano country were once known as dragon slayers and they did not want to waste any more soldiers and the government thought it might help them to get the wano country to join the world government. Due to the powerful samurai on the island the dragon could not leave unless they were defeated and the samurai could not return home without the dragons head. The constant fighting caused the dragon to remain on only half of the island causing the flames it put on the other half to go out and that half regained its frigid temperature and the samurai made this there half of the island only leaving when they attempted to take the dragons head. Although there are quite a few samurai on the island only one is on par with the dragon but he only fought the dragon a few times due to him being reluctant to go home to the wano country because he likes killing the foolish pirates or anyone who sets foot on the island but if he went back home he would not be allowed to do this but on the other hand he would lose his honor if he let the dragon escape so much to the other samurais dislike he is just content on keeping the dragon on the island. Even though the strongest samurai doesnt want to slay the dragon the other ones try to take its head on a regular basis but the leader doesnt care because he believes that he is the only one capable of taking the dragons head. But now the the Straw Hat Pirates arrive on the island and everything will change.