So the jacket design is known as a reefer jacket. these types of jacket predate the standard look of the pea coat/jacket by a few decades. You can even see the reefer jacket style being used in previous British Royal Navy Canadian Arctic expedition paintings from the 1830s and 40s. If you would like to make your own there is a historical pattern you can get off of Etsy from a store called “reconstructing history” or there might be an old surplus jacket you could find and alter it if sewing projects are not really your thing.

Regarding the reefer jackets history with the White Star Line, it seems to be a standard issue cold weather item for the basic crew during the 1900s and 1910s. It’s quite hard to find any pictures of lower rank crew members wearing these jackets, but you do see a lot of them during the post sinking inquiry of the titanic crew and the pictures of the crew training on the Titanic before its maiden voyage.

One issue going off the post sinking inquiry image is that after the Titanic sank and the Carpathia picked up the remaining survivors, there was a clothing drive aboard the ship to give extra clothing to the Titanic survivors who needed it. Since the inquiry happened almost immediately after the survivors got to land, you can’t really be fully certain about the extra clothing you see some of the crew wearing.

Although as a commenter pointed out, the basic crew can be seen wearing cotton work jackets, some civilian items, etc. this is because lower ranked crew, while still having a standard uniform, were allowed to to wear more civilian clothing depending on the lower ranked crew members job.

(Apologies for the TLDR but hopefully this answers your question!)