So first, read these two books in either order and practice the materials by going to meetups regularly:
How to Win Friends and Influence People by Dale Carnegie
How to Be a Gentleman by Jeff Bridges.
For book #1 you don’t need to focus too much on the persuasion, just focus on using it to get the formula behind social skills if you aren’t ready to learn actual SE yet to get prerequisites. For book #2, the other prerequisite book, make sure not to tell people you’re a gentleman as nothing is less gentlemanly or more gauche than a self-proclaimed gentleman. Otherwise, read those books and socialize a few times a week until the skills become natural and you’re doing it without even thinking about it. Then you can go to the next step.
Ok so now, once you’ve done that, start with one of Chris Hadnagy’s trainings of books. I recommend his online information elicitation course as it breaks down the basics of social engineering and you can practice it safely and ethically. Make sure to get the certification version of the course. Here’s a link to the course (its a around $200 depending on if you want to earn a cert by taking it):
https://www.social-engineer.com/information-elicitation/
Ok so do that course from beginning to end and use it to improve your social skills. The course is cumulative so you’ll need to do early chapters before moving onto later chapters. Don’t just listen to one chapter and move on tho. Listen multiple times, maybe once or twice a week with one chapter at a time, and socialize or practice the skills at work to slowly ingest it. Once the skills from that chapter become part of your personality, move onto the next chapter. Etc. Make sure to do all the course assignments and do a good job with every assignment and take notes on every chapter in addition to practicing it before you move onto the next chapter.
That’s it. If you want to learn body language and/or microexpressions, there’s tons of online free courses on that too so I’m not including that here but if your gonna do that, master the skills mentioned earlier here first. Otherwise, once you’ve done all of that, you should know a reasonable level of SE.