Sea shanties have been popular recently, but did other careers or guilds have work songs they sang? Are there any that moved into popular culture?

There most certainly are! I do need to address a couple things first though to get a little bit of context. First up is that a lot of songs commonly thought of as "shanties" (most notably "Wellerman") are not shanties. In an interview with Gerry Smyth, who recently wrote a book on the subject of sea shanties, he notes that the Wellerman does not have a chorus and was intended to be sung by a single person. I'm going to focus on those that are "actual" shanties as shanties had a specific purpose as a work song - colloquial shanties are a bit of a broader topic and it would be closer to asking "why do humans like music?" to include them.

Sea Shanties are a form of work song, and were used when a task required working in unison. This is a great video that demonstrates a halyard shanty and how it's used to coordinate hauling on a rope (e.g. if you're hoisting a sail). There are a whole slew of different types of shanties depending on the type of work. Halyard shanties are designed for tasks that require regular bursts of activity while other types of shanties (and there are quite a few) were designed for different work (e.g. Drunken Sailor was a "walk away" shanty where sailors would basically walk with slack ropes in unison).

There's a whole host of books on the subject of sea shanties but a (partially free) book English Folk-Chanteys by Cecil James Sharp is available online (and was a good source when looking more into this subject).

So what about other work? Well, the most direct comparison for work songs are military chants for marching. They use a similar call-and-response format to shanties with their chorus and are used to make sure everyone is moving in unison. These haven't found similar use in popular culture (outside of any media that depicts a bootcamp) - possibly because (and I should note this is 100% my speculation and I could not find a source for this) the chants typically involve repeated use of the words "left" and "right" to help with the march

Slightly further from sea shanties are agricultural work songs. Instead of being songs to keep people working in unison because the task demanded it (e.g. pulling a rope or marching), these songs were used to keep a good cadence and entertain during tasks that were monotonous. These most certainly have made their way into popular culture - most notably field songs sung by Black slaves in the United States. These songs typically followed a call-and-response style, and have widely been credited as the origins of numerous musical genres with gospel and blues being the most direct (America’s Black Musical Heritage by Tilford Brooks). These were split into two (very vague) categories. The first were similar to shanties and designed to keep people working in unison (whether that was reaping or rowing) while the other were for more general harvesting (e.g. picking corn or cotton) that didn't rely on keeping people in unison (The music of Black Americans : a history by Eileen Southern).

edit: /u/xdisk brought to my attention that there is more variation in cadence (what I called military chants) than I mentioned in this post; this is what they stated they observed in their time in the USMC:

Drill cadence isn't a 'call and response' type of work song, normally outside of training the platoon is not allowed to respond vocally. While in training recruits are taught verbal response to make sure they are doing their movements correctly and in time with others

The other type of cadence is running cadence. This type is call and response (at least in the USMC. The other branches can be different)

If someone knows more about the history of cadence in the US military (or any military) as well as the differences in type, feel free to chime in! I don't have many sources on it so I can speak to the use in the military in a broad sense but I don't have anything that discusses the differences between cadence or the variations between difference branches of the military (or variations by country for that matter).