Hello! I was in a very similar position before grad school. After learning how time consuming my administrative responsibilities would be, I was worried about having the time to do research. It ended up working out very well. In my experience, the skills you learn as a lab manager make you stand out during the application process. Most applicants can't speak to the everyday complexities of grant and IRB management.
With this said, you are right that it is also important to get experience with research. Once you are confident in your performance with your primary job, you could initiate a conversation with your PI about your desire to get more involved with research. My PI was very supportive. It turned out that some of the previous lab managers in my lab had been the most productive researchers and ended up with more publications than the RAs. But every setting is different. If your PI does not like the idea of you juggling your job with research, then this might be more challenging.
Nobody at interviews will ask you what percentage of time you spent on research, so as long as you have some research projects to discuss in your applications, you are golden. I always made sure I was working on one research project at a time. I often worked on research outside of work hours to ensure that I was making progress. I tried to make sure each project resulted in at least a poster. The importance of publications probably depends on how competitive the program is, but it's always a good goal.
Hope that helps a little!
