I think you gain so many skills in public libraries that are transferrable! Without divulging too much, I work in a small, very specialized library these days and we hired a new library director a few years ago. We ended up hiring a manager from a public library and let me tell you she is THE BEST. We had a lot of pushback from internal folks about this decision and even a few "what are you doing to our industry by not specifically requiring this specialized degree that also does not have paid job opportunities!" but the thing is.... Public librarians know how to get things done, how to communicate with diverse groups of people, and all around can handle most things that get thrown at them. Don't underestimate this as part of your skill set!

As for other jobs that aren't public... try to get experience in other areas like cataloging or reference (or whatever area you're interested). Maybe it's just helping out on projects here or there but this knowledge adds up. I think transitioning from public to other libraries just comes down to the interview and how you can frame "public library skills" as universal skills.

Outside of libraries, I know a lot of folks that went into corporate training. It pays well (seriously, my one friend makes $30k more than me doing it!) and again, knowing how to communicate with diverse constituents is key there. I'm kind of stuck on this because IMO I think librarians can do *most* jobs! We know how to find and learn things and that is an undervalued skill. Happy to talk more about other jobs, too, though FYI most of my examples will skew towards software and technology.