How best would you take charge of your learning and career in a job that gives little or no room for you to pursue your own learning?

You back off your commitment to the job to some level that won't get you dismissed, then, in your own time, you develop skills and competencies for whatever area interests you. For interview purposes, you can always say that the projects you worked on were internal - make sure you have got something like the level of ability that comes with completing a real project though!

You need to use your free time to learn and create projects, so you can upskill and find a better job.
You can also try to think about little improvements you can implement on your daily routine, and offer some suggestions to your team or management, based on what you learned.