Well, I kinda went a different route, starting with animation, transitioning into game design and then from there into coding, mostly to be able to work on my own hobby projects.
When we started out, none of us had any design education but we did have some experience in game creation, like modding, hobby projects in game maker etc. I think this can often be just as useful as studying design and in many cases give you a more realistic idea of what game design is. So my tip is to just start making games in an accessible engine like Unity or Defold and start exploring your ideas. Also, once you start looking for a design-job, it doesn’t hurt to have personal game projects in your portfolio.
Since you are already proficient in programming you have the advantage of being able to dive right into creating your own games where you can play around with ideas, and learn what works for you and what doesn’t. If you have someone to bounce design ideas with that usually helps a lot.
You’ll eventually discover, if you haven’t already, what kinds of design (game mechanics, AI, levels, narrative etc.) that you are more into as well as what genres appeal to you the most. You might be drawn to sandboxy Rockstar games, maybe you’re a fan of clean minimalist Blizzard-esque design, or perhaps number crunchy spreadsheet-games are your thing. You don’t have to, and maybe shouldn’t, place yourself squarely into a niche, but a strong sense of identity in your design helps you find the right studio for you and increases your chances of landing the job.
I hope that piece of contradictory advise was to some help. Otherwise, keep asking and I’ll try again