I don't really know what people are doing to enrich their vocabulary and fluff up their language to be honest; my vocabulary and writing all stem from high school. However, my experience is that in order to write well, you need to read a lot. Learn what works for others, consider why it may not work for you, and pick up the good bits. If all else fails, open a dictionary, pick a word every day, and try to use it in a sentence before going to bed, just so you learn more synonyms and specific terms.
I'm pretty sure that when it comes to job applications, most people are probably using AI these days. Unless you think you can beat AI, it doesn't hurt to let the some kind of AI go over your text and steal some or the good bits.